A theatre has three types of seating. Ticket prices are shown below.

(a) Find the ratio of ticket costs stalls : circle : private box, in its simplest form. [2]

(b) A website charges a fee of 5% of the cost of each ticket. Arshad buys 2 stalls tickets and 3 circle tickets. Work out the total cost, including the fee. [3]

(c) There are 1200 stalls seats. One evening, \(\frac56\) of these tickets are sold. Tickets sold for stalls : circle are in the ratio \(10:7\). Find the number of circle tickets sold. [3]

Express \(\$30\) as a percentage of \(\$120\). [2]

A car originally costs \(\$23000\). Its value decreases by \(35\%\) of the original value. Find its new value. [2]

Work out \(55\%\) of \(12.2\). [1]

Yasmin has a collection of coins. \(10\%\) are gold; \(25\%\) of the remaining coins are silver. The other 54 coins are copper.

(a) Find the number of silver coins. [2]

(b) Find the total number of coins. [2]

Ruta and Zoli share money in the ratio \(7:3\). Ruta receives \(\$420\) more than Zoli. Find how much each receives. [3]

A sewing machine is reduced by \(\$38\), which is an \(8\%\) reduction in its original price. Find the original price. [2]

A shirt is reduced by \(15\%\). Its sale price is \(\$23.63\). Find the original price. [2]

Hadi can buy a dishwasher with a single payment of \(\$980\), or a monthly plan: \(20\%\) of \(\$980\) plus 12 payments of \(\$75.25\).

(a) Find the total amount paid with the monthly plan. [2]

(b) Find the percentage increase compared with the single payment. [2]

The masses of boxes A and B are in the ratio 4:7. B is 2.4 kg heavier than A. Find both masses. [3]

Divide \(\$90\) in the ratio 2:3. [2]

A computer costs \(\$560\). Its price is reduced by 20% in a sale. Find the sale price. [2]

Write the ratio 60 grams : 3 kilograms in the form \(1:n\). [2]

Coat prices are reduced by 15% in a sale.

(a) Find the sale price of a coat originally costing \(\$60\). [2]

(b) Another coat has sale price \(\$58.14\). Find its original price. [2]

Pedro makes cards.

(a) He makes 9 cards every 20 minutes. Work out how many cards he makes in 8 hours. [2]

(b) Each card costs 12 cents to make and sells for 50 cents. Work out the percentage profit on each card. [2]

A dressmaker takes 75 hours to make 31 dresses. In week 1 she takes 12 hours 30 minutes to make the first 4. In week 2 she makes the remaining 27 at a constant hourly rate. Find the percentage increase in her hourly rate. [4]

m is a positive integer. Order these from smallest: \(m\), 33% of m, \(\frac13\) of m, 320% of \(\frac m{10}\). [2]

A grocer sells potatoes, mushrooms and carrots.

(a) Find the cost of 3 kg of mushrooms at \(\$1.04\)/kg and 4 kg of carrots at \(\$1.28\)/kg. [2]

In one week, masses sold are in the ratio potatoes:mushrooms:carrots=11:8:6.

(b(i)) Find the mushroom mass as a percentage of the total. [2]

(b(ii)) Total mass sold is 1500 kg. Find the carrot mass. [2]

(b(iii)) Profit is \(\$0.75\) per kilogram of carrots. Find the total carrot profit. [1]

(b(iv)) Potatoes are reduced by 8% to \(\$1.15\)/kg on the last day. Find the original price per kilogram. [2]

(c) 620 kg of onions, to the nearest 20 kg, is packed into bags each containing 5 kg, to the nearest kilogram. Find the upper bound for the number of bags. [3]

(a(i)) Find Valdivian area as a percentage of Amazon area. [1]

(a(ii)) Simplify Valdivian:Atlantic:Congo. [2]

(a(iii)) 60% of Amazon is in Brazil and 10% in Colombia. \(43\frac13\%\) of the remaining area is in Peru. Find the percentage in these three countries combined. [3]

(a(iv)) Amazon is \(\frac{27}{50}\) of the world rainforest area. Find the total, to the nearest 100000 km². [3]

(a(v)) 60.7 hectares are lost each minute. Find the area lost in 365 days, in standard form. [3]

(b) Amazon river is 6440 km to the nearest 10 km; Congo river is 4400 km to the nearest 100 km. Find the upper bound of their length difference. [3]

(a) A drink uses 1.5 litres apple juice and 450 ml mango juice. Simplify apple:mango. [2]

(b) One litre is divided between cups in ratio 9:6:10. Find each amount in ml. [3]

(c) A shop buys bottles for \(\$3.20\) and sells at 15% profit. Find the selling price. [2]

(d) Sales grow exponentially by 2.5% annually. Five years ago 16620 bottles were sold. Find this year’s sales. [2]

(e) Bottles are 18.5 cm tall to the nearest millimetre; shelf spacing is 23 cm to the nearest centimetre. Find the lower bound of clearance d. [3]

In 2023 a football club had 50 adult and 70 child members. Fees were \(\$40\) per adult and \(\$15\) per child.

(a(i)) Find the total fees received. [2]

(a(ii)) Running costs were \(\$2780\). Express this as a percentage of fees received. [1]

(a(iii)) The 120 members in 2023 represented a4% decrease from 2022. Find the 2022 membership. [2]

(a(iv)(a)) In 2024 adults and children each increased by the same number. Adult:child ratio became 14:19. Find total 2024 membership. [2]

(a(iv)(b)) Find the percentage increase from 2023 to 2024. [2]

A village has population 2500, decreasing exponentially by 3% annually.

(b(i)) Find the population after 3 years. [2]

(b(ii)) Find the first complete year when population is below 2000. [2]

Safia cuts 5.6 m of fabric into lengths in the ratio 3:4. Find the longer length. [2]

(a(i)) Anvi buys a \$28240 car with a 7.5% discount. Find the amount paid. [2]

(a(ii)) Her new 45-litre fuel tank is 72% of her old tank capacity. Find the old capacity. [2]

(b) Aadi buys a \$28000 car using a finance plan: deposit, 47 monthly payments of \$330, and a final \$11490 payment. He pays \$31900 in total. Find the deposit as a percentage of \$28000. [4]

(c) A car covers 64 km using 2.5 litres, then 128 km using 6 litres. Find the whole-journey fuel use in litres per 100 km. [2]

(d) A car worth \$46500 at the start of 2021 loses 20% during 2021, then 15% of its remaining value during 2022. Find its value at the end of 2022. [2]

(a) Dinari sells fruit and vegetables. One day their masses are in the ratio fruit:vegetables=9:8. He sells 48 kg of vegetables. Find the mass of fruit sold. [2]

(b) The amounts received for fruit and vegetables are \((c+3)\) dollars and \((c-1)\) dollars respectively, giving the ratio \((c+3):(c-1)\). Their total is \$280. Find the money received for fruit. [3]

(c) In one week Dinari buys fruit and vegetables for \$1620 and sells them for \$1750. Find the percentage profit. [2]

(d) In another week Dinari sells fruit and vegetables for \$1738 at a profit of 10%. Find the amount he paid for them. [2]

A map scale is \(1:125000\). An island is 9.4 cm long on the map.

Calculate its actual length in kilometres. [2]

A map distance is 3.5 cm and its scale is \(1:250000\).

Find the actual distance in kilometres. [2]

A shopkeeper has 12 tins of cat food left, which is \(3/13\) of his original number.

Find his original number of tins. [2]

An orchard has 1250 trees, in the ratio apple : pear : cherry = \(12:9:4\).

(a(i)) Calculate the number of apple trees. [2]

(a(ii)) Last year the mean fruit mass was 64 kg per tree. Calculate the total fruit mass in tonnes. \(1\text{ tonne}=1000\text{ kg}\). [2]

(a(iii)) Last year the mean mass of pears per pear tree was 54 kg, a decrease of 10% on the previous year. Find the mean for the previous year. [2]

(a(iv)) A storm destroys \(1/5\) of all the trees. How many remain? [2]

(b(i)) Pears at a market cost \$0.54 each or 0.51 euros each. Paulo pays in dollars for 12 pears. Calculate his change from \$10. [2]

(b(ii)) The exchange rate is \$1 = 0.826 euros. How much more does each pear cost when he pays in euros? Give the difference in dollars, to the nearest cent. [3]

Tomas sells a computer, bike and phone. The amounts received have ratio computer : bike : phone = \(14:17:9\).

(a(i)) Find the phone amount as a percentage of the total. [2]

(a(ii)) The total is \$560. How much does he receive for the bike? [2]

(a(iii)) He bought the bike for \$195 and wanted a profit of at least 25%. Does he achieve this? Show working supporting your decision. [3]

(b) Ulla invests \$725 for 6 years at 1.3% simple interest per year. Find the total interest. [2]

(c) Sale prices are reduced by 24%. Victor pays \$36.86 for shoes. Find their original price. [2]

Oliver sends 22% more messages in June than in May. He sends 305 in June. How many more messages does he send in June? [3]

At the end of 2021 there are 27 000 wild rhinos. The number decreases exponentially by 3% each year. Find the expected number at the end of 2025, to the nearest whole number. [3]

(a) A company employed 300 workers initially and now employs 852. Find the percentage increase. [2]

(b) Its 852 workers have ratio part-time : full-time = 5:7. Find the full-time count. [2]

(c(i)) The company makes 40600 headphones yearly. Write this number in words. [1]

(c(ii)) Write it in standard form. [1]

(d) Of 3000 headphones sold in one month, 48% are exported, \(3/8\) go to shops and the rest are sold online. Find the online count. [3]

(e) Sales rise 15% one year and 18% the next. Find the overall percentage increase. [3]

A \$126 coat is reduced by 18%. Find its sale price. [2]

(a) Alex, Bobbie and Chris share strawberries 3:2:2. Chris receives 12. Find the total. [2]

(b(i)) A shop reduces prices 12%. Find the sale price of a \$6.50 book. [2]

(b(ii)) A toy costs \$11 in the sale. Find its original price. [2]

(c) Feri’s investment earns 2.5% in year one. After year two its overall increase is 6.6%. Find the year-two rate. [2]

(d(i)) An 80 g radioactive mass decays exponentially by 2% daily. Find its mass after 5 days. [2]

(d(ii)) Find how many more whole days after day 5 are needed for mass below 67 g. [3]

Wild tiger populations in 2014:

(a(i)(a)) Find Nepal’s population as a percentage of Bangladesh’s. [1]

(a(i)(b)) Find Bangladesh:Indonesia:India in its simplest form. [2]

(a(ii)) Five years later India has 2967 tigers. Find the percentage increase. [2]

(a(iii)) India’s 2014 population is approximately 30.48% greater than in 2010. Find the 2010 population to the nearest integer. [3]

(b) A hive starts June with 2000 bees and has 2662 after 3 months. Its population after x months is \(P=ab^x\). Find a and b, then its population after 7 months to the nearest integer. [5]

Divide \$200 in the ratio 7:3. [2]

A \$520 computer is reduced by 15%. Find the sale price. [2]

(a(i)) Football season ticket costs are in the ratio seated : standing = 5 : 3. A standing ticket costs \$45. Find the seated ticket cost. [2]

(a(ii)) The team’s players were valued at \$2.65 million in 2021. This decreased by 12% in 2022. Find the 2022 value in millions of dollars. [2]

(a(iii)) An attendance of 1455 is 6.25% of the stadium capacity. Find the capacity. [2]

(a(iv)) Average attendance increased exponentially by 4% each year from 2016 to 2019. In 2019 it was 1631. Find the 2016 average attendance. [3]

(b(i)) Another club’s 2018 ticket sales were in the ratio family : individual = 2 : 7. There were x family tickets. Express the number of individual tickets in terms of x. [1]

(b(ii)) In 2019 family ticket sales increased by 12 and individual ticket sales decreased by 26. Write expressions for each number in 2019. [2]

(b(iii)) In 2019 individual tickets sold were three times family tickets sold. Form and solve an equation to find x. [4]

A pasta bake for 12 people needs 250 g butter, 600 g pasta, 460 g mushrooms, 280 g cheese and 800 ml milk.

(a(i)) Find the cheese mass as a percentage of the mushroom mass. [1]

(a(ii)) Find the butter needed for 18 people. [2]

(a(iii)) Monica has 2.2 litres of milk and 1.5 kg of each other ingredient. Find the greatest number of people she can serve. [3]

(b(i)) A pasta packet cost \$2.40 in 2019, 25% more than in 2018. Find the 2018 cost. [2]

(b(ii)) In 2020 the cost increased by another 15%. Find the total percentage increase from 2018 to 2020. [3]

(c) Packet width is 11.5 cm to the nearest 0.5 cm. Shelf length is 2 m to the nearest 0.1 m. Find the maximum number of packets that fit in a single line, showing working. [3]

Sahil and Anika share \$78 in the ratio 5 : 8. Find each share. [2]

A taxi charges \$0.50 per kilometre plus \$0.40 per minute.

(a(i)) Find the cost of a 32 km journey taking 30 minutes. [2]

(a(ii)) A 100 km journey costs \$98. Show that it takes 2 hours. [3]

(b) Three drivers travel 8190 km in the ratio 5 : 2 : 7. Find each distance. [3]

(c) After midnight, all taxi costs rise by 45%. One journey then costs \$84.10. Find its cost before midnight. [2]

A 2.5-litre tin of paint costs \$13.50 and is reduced by 14% in a sale.

(a(i)) Find its sale price. [2]

(a(ii)) Find the cost of 42.5 litres at the sale price. [2]

(b(i)) Henri buys red : white : green paint in the ratio 2 : 8 : 5. Find the percentage that is white. [1]

(b(ii)) He buys 22.5 litres in total. Find the green paint volume. [2]

(c) Maria paints a rectangular wall of length 20.5 m and height 2.4 m, both correct to 1 decimal place. Exactly 1 litre covers 10 m². Find the smallest number of 2.5-litre tins needed to be sure of covering the wall. Show working. [4]

(a(i)) Yasmin and Zak share money in the ratio 21 : 19. Yasmin gets \$6 more. Find the total. [2]

(a(ii)(a)) Sale prices are 15% lower. Find the sale price of a \$40 blouse. [2]

(a(ii)(b)) A shirt costs \$29.75 in the sale. Find its original price. [2]

(b(i)) Xavier’s salary increases by 2% annually. It was \$40 100 in 2010. Find his salary in 2015 to the nearest dollar. [3]

(b(ii)) Find the first year his salary exceeds \$47 500. [3]

(c) A town’s January 2020 population was 5% above January 2018. In January 2021 it was 2% below January 2020. Find the overall percentage increase. [2]

Write 26 g as a percentage of 208 g. [1]

A train fare increases by 6% to \$153.70. Find its original cost. [2]

Jo and Mo share \$26. Jo receives \$5 more than Mo. Find Jo : Mo in simplest form. [3]

Marek buys a computer for \$420 and sells it at a loss of 15%. Find the selling price. [2]

Chai invests some money. Its value decreases by 35% in the first year, then increases by 40% of its value at the end of the first year. Find the overall percentage change. [3]

Bob, Chao and Mei take part in a charity run. Their times have ratio Bob : Chao : Mei = 4 : 5 : 7.

(a(i)) Find Chao’s time as a percentage of Mei’s. [1]

(a(ii)) Bob takes 55 minutes 40 seconds. Find Mei’s time in minutes and seconds. [3]

(b(i)) Chao collects \$47.50. Bob collects 28% more. Find Bob’s amount. [2]

(b(ii)) Chao collects 60% less than Mei. Find how much more Mei collects than Chao. [3]

(c) Chao’s stride is 70 cm to the nearest 5 cm. The distance is 11.2 km to the nearest 0.1 km. Find the minimum number of strides needed. [4]

(d) A charity raises \$1.6 million in 2015. It increases by 2.4% each year for five years. Find the 2020 amount in millions of dollars. [2]

Malena has 450 fruit trees in the ratio apple : pear : plum = 8 : 7 : 3.

(a(i)) Show that she has 200 apple trees. [2]

(a(ii)) Find the number of plum trees. [1]

(a(iii)) She wants 32% more pear trees. Find how many extra pear trees she needs. [2]

(a(iv)) Each apple tree produces 48.5 kg of apples of average mass 165 g. Find the total number from 200 trees, to the nearest 1000. [3]

(b(i)) Her land is valued at three million and seventy-five thousand dollars. Write this in figures. [1]

(b(ii)) Write the value in standard form. [1]

(c) Each plum tree produced 37.7 kg in 2020, 16% more than in 2019. Find its 2019 yield. [2]

(d) She invests \$1800 at 2.1% compound interest per year. Find its value after 15 years. [2]

Roberto buys a toy for \$5.00 and sells it for \$4.60. Find his percentage loss. [2]

(a(i)) Gretal earned \$32000 in 2018 and paid tax of 24%. Find her tax. [2]

(a(ii)) Her earnings increased by 7% in 2019. Find her 2019 earnings. [2]

(b) Gretal invests \$5000 at 2% yearly compound interest. Find its value after 3 years. [2]

(c) She spends \$360 on presents: 1/5 on her parents, then 2/3 of the remaining money on friends, and the rest on sisters. What percentage of \$360 is spent on her sisters? [4]

(d) Arjun earned \$36515 in 2019, an increase of 9% on 2018. Find his 2018 earnings. [2]

(e) Rent ratios Arjun : Gretal were 5 : 7 in 2018 and 9 : 13 in 2019. Arjun paid the same amount both years; Gretal paid \$290 more in 2019. Find Arjun’s rent in 2019. [4]

Daily campsite fees: tent \$15; caravan \$25.

(a) Today there are54 tents and18 caravans. Find the total fees. [2]

(b) September income was \$37054, a decrease of4.5% from August. Find August’s income. [2]

(c(i)) Visitor ratios are men : women =5 :4 and women : children =3 :7. Find men : women : children in simplest form. [2]

(c(ii)) There are224 children. Find the total number of men and women. [3]

(d) Each tent space is a rectangle8 m by6 m, each dimension correct to the nearest metre. Find the upper bound of its area. [2]

(e) Campsite value has increased exponentially by1.5% yearly for30 years. Find its present value as a percentage of its value30 years ago. [2]

(a) Choose the correct calculation for increasing40 by300%: \(40\times1.300,\quad40\times3,\quad40\times400,\quad40\times4,\quad40\times300\). [1]

(b) Choose the magnitude calculation for \(\begin{pmatrix}2\\-3\end{pmatrix}\): \(\sqrt{2^2+-3^2},\quad2^2-3^2,\quad\sqrt{2^2-3^2},\quad2^2+(-3)^2,\quad\sqrt{2^2+(-3)^2}\). [1]

Alex and Chris share sweets in the ratio7 :3. Alex receives20 more than Chris. Find Chris’s share. [2]

Increase42 by16%. [2]

Adil and Brian initially have the same wage. After a7% decrease Adil earns \$427.80; Brian gets a7% increase. Find Brian’s new wage. [3]

(a) A plane has 14 First Class, 70 Premium and 168 Economy seats. Give First Class : Premium : Economy in its simplest form. [2]

(b(i)) Morning ticket prices have ratio First Class : Premium : Economy = 14 : 6 : 5. Premium costs \$114. Find First Class and Economy prices. [3]

(b(ii)) An afternoon Premium ticket is reduced from \$114 to \$96.90. Find the percentage reduction. [2]

(c(i)) When Athens local time is 09:00, Berlin local time is 08:00. A plane leaves Athens at 13:15 and arrives in Berlin at 15:05 local time. Find the flight time. [1]

(c(ii)) It flies 1802 km. Find its average speed in km/h. [2]

The Earth’s surface area is approximately 510100000 km².

(a(i)) Write it in standard form. [1]

(a(ii)) Water covers 70.8% of the surface. Find the area covered by water. [2]

(b(i)) Find the total surface area of Brunei and the Maldives. [1]

(b(ii)) Maldives area : China area =1 : n. Find n. [2]

(b(iii)) Find France’s area as a percentage of China’s area. [2]

(b(iv)) Find the population density of the Maldives (population ÷ area). [2]

Earth’s estimated population was \(7.53\times10^9\) in 2017 and \(6.02\times10^9\) in 2000.

(c(i)) Find the percentage increase from 2000 to 2017. [2]

(c(ii)) Assume exponential growth at y% annually for these 17 years. Find y. [3]

A train’s passenger count increases from63 to77. Find the percentage increase. [3]

Amol and Priya deliver645 parcels in the ratio Amol :Priya=11 :4.

(a) Find the number Amol delivers. [2]

(b) Amol drives at50 km/h from07:00 to11:15. Find the distance. [2]

(c) Priya drives54 km from10:55 to12:38. Find her average speed in km/h. [3]

(d) Priya has50 identical parcels of mass17 kg each, correct to the nearest kilogram. Find the upper bound of their total mass. [1]

(e) 67 parcels are damaged. Find the percentage damaged. [1]

(f(i)) 29 parcels are worth \$68 each. Round both numbers to1 significant figure to estimate their total value. [1]

(f(ii)) Without calculating, explain why the actual value is less than this estimate. [1]

Work out \$1.20 as a percentage of \$16. [1]

Shona buys a chair for \$435.60 in a sale, a reduction of 12% from its original price. Calculate the original price. [3]

(a) A newspaper rises in price from \$0.97 to \$1.13. Find the percentage increase. [3]

(b) A60-page newspaper has news pages:advertisement pages=5:7.

(b(i)) Find the number of advertisement pages. [2]

(b(ii)) Express advertisement pages as a percentage of news pages. [1]

(c) Maria pays €2.25 for a newspaper abroad at \$1=€0.9416; at home it costs \$1.13. Find the price difference in dollars to the nearest cent. [3]

(d) Annual newspaper sales decrease exponentially by x%. In21 years sales fall from1763000 to58000. Find x. [3]

(e) Each page measures43 cm by28 cm, both to the nearest centimetre. Find the upper bound of its area. [2]

Find 5% of \$25. [1]

(a) Ali and Mo share money in the ratio 9:7. Ali receives \$600 more. Find each share. [3]

(b) Ali buys a television for \$195.80, reduced from \$220. Find the percentage reduction. [3]

(c) Mo buys a jacket for \$63 after a 25% reduction. Find the original price. [3]

Mohsin has 600 pear trees and 720 apple trees.

(a(i)) Write pear trees : apple trees in simplest form. [1]

(a(ii)) Each apple tree produces 16 boxes annually, each containing 18 kg. Find the total annual mass from 720 trees in standard form. [3]

(b(i)) One week 18 540 kg of pears are picked. The mass ratio apples : pears is 13:9. Find the apple mass. [2]

(b(ii)) The apples cost \$0.85/kg to produce and sell at 60% profit. Find the selling price per kg. [2]

(c) A Belgian shop buys pears at \$1.50/kg and sells them at €2.30/kg. The rate is \$1 = €0.92. Find its percentage profit. [5]

(d) Mohsin’s earnings increase by 8.7% annually. He earned \$195 600 in 2018. How much more does he earn in 2027? [3]

A cycling club has males : females = 8:3 and 342 female members.

(a(i)) Find the total membership. [2]

(a(ii)) Find the percentage of members who are female. [1]

(b) A bicycle costs \$1020 before a 15% club discount. Find the price for a member. [2]

(c) Membership costs \$79.50 in 2019, 6% more than in 2018. Find the increase in cost. [3]

(d) Asif cycles 60 km in 2 h 24 min, then 45 km at 20 km/h. Find his average speed for the whole 105 km. [4]

(e) Bryan invested \$480 four years ago at 2.1% annual compound interest. Today he buys a \$430 bicycle from the account. How much remains? [3]

(f) \(s=\frac12at^2\). Values a=3 and t=10 are each rounded to the nearest integer. Find the lower bound of s. [2]

Dev makes 600 cakes. 18% go to a hotel and 2/3 to a supermarket. How many are left? [3]

Increase \$22 by 15%. [2]

Adele, Barbara and Collette share \$680 in the ratio 9:7:4.

(a) Show that Adele receives \$306. [1]

(b) Find Barbara’s and Collette’s shares. [3]

(c) Adele exchanges \$306 at €1=\$1.125. How many euros does she receive? [2]

(d) Barbara spends \$17.56 on 5 kg of apples and 3 kg of bananas. Apples cost \$2.69/kg. Find the price of bananas per kilogram. [3]

(e) Collette spends half her share on clothes and one-fifth on books. Find the amount left. [3]

20 biscuits need 260 g butter, 500 g sugar, 650 g flour and 425 g rice.

(a(i)) Find rice mass as a percentage of sugar mass. [1]

(a(ii)) Find butter needed for 35 biscuits. [2]

(a(iii)) Michel has 2 kg of each ingredient. Find the greatest number of biscuits he can make. [3]

Packets cost \$1.35 to make and sell for \$1.89.

(b(i)) Find the percentage profit on each packet. [3]

(b(ii)) \$1.89 is 8% more than last year’s price. Find last year’s price. [3]

(c) Sales grew from 15.6 million to 20.8 million packets in 3 years, at the same annual percentage rate. Find that rate. [3]

Employee groups: A under 30, B aged 30–50, C over 50. A:B=7:10 and B:C=4:3.

(d(i)) Find A:C in simplest form. [3]

(d(ii)) There are 45 in C. Find the total number of employees. [3]

Work out \$1.45 as a percentage of \$72.50. [1]

Marianne sells photos.

(a(i)) Each sells for \$6; printing cost:profit=5:3. Find her profit per photo. [2]

(a(ii)) Find profit as a percentage of selling price. [1]

(a(iii)) Convert the selling price to euros at €1=\$1.091. [2]

(b) Similar rectangular photos: smaller 15 cm by 12 cm; larger area 352.8 cm². Find the larger length. [3]

(c) A camera costs \$483 after an 8% reduction. Find the original price. [3]

The Muller family are on holiday in New Zealand.

(a(i)) They receive NZ\$1962 at €1=NZ\$1.635. Find the euros exchanged. [2]

(a(ii)) They spend 15% on a tour. Find the dollars left. [2]

(a(iii)) Humboldt Falls:Bridal Veil Falls height ratio=5:1. Humboldt is 220 m higher. Find Humboldt’s height. [2]

(b(i)) Browne Falls flow rises from 3680 to 9752 litres/s. Find the percentage increase. [3]

(b(ii)) Sutherland Falls flow is 74 240 litres/s after a 45% increase. Find its previous flow. [3]

240 students; girls:boys=25:23.

(a(i)) Show there are 115 boys. [1]

(a(ii)) 15 girls and 15 boys are absent. Find girls:boys present, in simplest form. [2]

(a(iii)) Next year numbers rise 15%. Find the new total. [2]

(a(iv)) Current 240 is 60% above the number when the school opened. Find the original number. [3]

(b) A city population 256000 rises 2% annually. Find population after 30 years to nearest thousand. [3]

(c) Bacteria grow r% per day. After 32 days the population has increased 309%. Find r. [3]

Indira buys a television for \$924 in a sale, a reduction of 12% on the original price. Calculate the original price. [3]

Work out 85 cents as a percentage of \$2.03. [1]

Write 55 g as a percentage of 2.2 kg. [2]

Fuel costs \$0.88 per litre in May 2015, 20% less than May 2014. Find the May 2014 price. [3]

Write \$450 as a percentage of \$680. [1]

(a) A library has 10494 fiction and non-fiction books in ratio 13:5. Find the number of non-fiction books. [2]

(b) Crime : adventure : science-fiction DVDs =11:6:10. There are 384 more science-fiction than adventure DVDs. Find the crime DVD count. [2]

(c(i)) Sima drives 20 km to the library in 23 minutes. Find her average speed in km/h. [2]

(c(ii)) One Monday her average speed is only 32 km/h. Find the percentage increase in journey time. [5]

(d) The same book costs €11.99 in Spain and \$12.99 in the USA. \$1=€0.9276. Find the price difference in dollars to the nearest cent. [3]

(e) 7605 books were borrowed in 2016, 22% fewer than in 2015. Find the number borrowed in 2015. [3]

Aasha, Biren and Cemal share \$640 in the ratio \(8:15:9\).

(a) Show that Aasha receives \$160. [1]

(b) Find the amounts Biren and Cemal receive. [2]

(c) Aasha spends her \$160 on books costing \$15.25 each. Find the greatest number she can buy. [2]

(d) Biren spends \(\frac38\) of his share on clothes and \(\frac13\) on a computer. Find the fraction left, in lowest terms. [3]

From a sample of 80 batteries, 3 are faulty.

Work out the percentage of faulty batteries. [1]

Mr Chan flies 8800 km from London to Los Angeles in 11 hours 10 minutes.

(a(i)) He leaves London at 09:35 local time. Los Angeles is 8 hours behind London. Find his arrival time in Los Angeles. [2]

(a(ii)) Find the average speed in km/h. [2]

Ticket prices are in the ratio economy : business : first class = \(2:5:9\).

(b(i)) A business ticket costs \$2350. Find the price of a first class ticket. [2]

(b(ii)) Express the economy price as a percentage of the first class price. [1]

Another airline charges \$2240 for a business ticket on the same journey.

(c(i)) Its first class ticket is 70% more than business. Find the first class price. [2]

(c(ii)) Its business ticket is 180% more than economy. Find the economy price. [3]

Mr Chan hires a car. Hire costs \$28 per day plus \$6.50 per day insurance. The first 800 km are included; each kilometre after 800 km costs \$1.25. He hires it for 12 days and pays \$826.50.

(d(i)) Find the number of kilometres travelled. [4]

(d(ii)) The car uses 1 litre of fuel per 10 km. Fuel costs \$1.30 per litre. Find his fuel cost. [2]

A football club sells tickets at different prices according to age.

For one game, ticket numbers are in the ratio under 18 : 18 to 60 : over 60 = \(2:7:3\). There are 6100 under-18 tickets.

(a(i)) Find the total number of tickets. [3]

(a(ii)) Find the percentage of under-18 tickets. [1]

For a different game, 42600 tickets are sold: 14% to people under 18, \(\frac23\) to people aged 18 to 60, and the remainder to people over 60.

(b) Find the total ticket revenue for this game. [5]

A shirt has sale price \$23.80, calculated incorrectly using a 30% reduction instead of the intended 20% reduction.

(c) Find the correct sale price. [5]

Ahmed bought a car for \$34000. Its value fell 40% after the first year, then fell another 10% in the second year.

Find its value after two years. [2]

Ralf and Susie share \$57 in the ratio 2 : 1.

(a) Find the amount Ralf receives. [2]

(b) Ralf gives \$2 to Susie. Find the new ratio Ralf : Susie, in simplest form. [2]

A jigsaw puzzle has edge pieces and inside pieces in the ratio 3 : 22.

(a(i)) There are 924 inside pieces. Calculate the total number of pieces. [2]

(a(ii)) Find the percentage of the pieces that are edge pieces. [1]

(a(iii)) Anjum and Betty spend a total of 9 hours completing the puzzle. Their times are in the ratio 7 : 5. Find Anjum’s time. [2]

(b) The puzzle costs \$15.99 in a sale, 35% below its original price. Calculate its original price. [3]

(c) A photograph and the completed puzzle are mathematically similar. Their areas are 875 cm² and 2835 cm² respectively. The photograph is 35 cm long. Find the length of the puzzle. [3]

(d(i)) Convert the area 6610 cm² of another puzzle to m². [1]

(d(ii)) This puzzle costs \$12.50 and sells for \$18.50. Calculate the percentage profit. [3]

Ahmed, Batuk and Chand share \$1000 in the ratio 8 : 7 : 5. Calculate each share. [3]

Olton’s population falls by 3% yearly. It was 50000 in 2013. Calculate the population after 4 years, to the nearest hundred. [3]

Ahmed and Babar share 240 g of sweets in the ratio 7 : 3. Find Ahmed’s share. [2]

A coat is reduced from \$85 to \$67.50. Find the percentage reduction. [3]

12000 vehicles use a road toll in one day. Cars : trucks : motorcycles = 13 : 8 : 3.

(a(i)) Show that there are 6500 cars. [1]

(a(ii)) Calculate the number of trucks. [1]

(b) Show that total tolls for the day are \$34500. [2]

(c) This is 8% less than the amount on the same day in 2013. Find the 2013 amount. [3]

(d) 2750 of the 6500 car drivers pay by credit card. Find their fraction in simplest form. [2]

(e) 90000 cars use the toll in a week, to the nearest thousand. Write the lower bound. [1]

(a) A golf club charged \$1650 for family membership last year. This year it increases by 12%. Find the new cost. [2]

Competition prizes are shared in the ratio first : second = 9 : 5. First prize is \$500 more than second prize.

(b(i)) Find the total prize money. [2]

(b(ii)) What percentage is first prize? [1]

For club members, men : children = 11 : 2 and women : children = 10 : 3.

(c(i)) Find men : women. [2]

(c(ii)) There are 24 children. Find the total number of members. [3]

(d) Golf balls sell for \$20.40, with profit of 20% of cost price. Find the cost price. [3]

Pip and Ali share \$785 in ratio Pip : Ali = 4 : 1. Find Pip’s share. [2]

Jason spends \(11/15\) of his birthday money and has \$14.40 left. Find the amount received. [3]

Jasjeet gives her brother 1% of her stamps and has 2475 left. Find her original number. [3]

(a) Luc uses \(3/4\) of a tin of paint per door. Find the least number of tins needed for 7 doors. [3]

(b) Jan buys paint for \$17.16 per tin and sells it at 25% profit. Find the selling price. [2]

(c) \$17.16 is 4% more than last year’s cost. Find last year’s cost. [3]

(d) A tin costs \$17.16 in America and €13.32 in Italy. The exchange rate is \$1 = €0.72. Find the price difference in dollars. [2]

Cylindrical tins are 11 cm high and hold 750 ml.

(e(i)) Write 750 ml in cm³. [1]

(e(ii)) Find the tin radius, to 1 decimal place. [3]

(e(iii)) A similar tin has height 22 cm. How many litres does it hold? [2]

(f) A tin’s mass is 890 g to the nearest 10 g. Find the upper bound of the total mass of 10 tins. [1]

(g) The probability a tin is dented is 0.07. How many dented tins are expected among 3000? [2]

(h) Tins are filled at 2 m³ per minute. How many 750 ml tins can be filled in an hour? [3]

512 actors are in the ratio men : women : children = 7 : 11 : 14.

(a(i)) Show that there are 224 children. [2]

(a(ii)) Find the number of men. [1]

(b) Each child is given \$1 every working day and works for 45 days. Find the total given to the children, to the nearest \$100. [2]

(c) Children have lessons in groups of no more than 12. Find the smallest number of groups. [2]

The film costs four million and ninety three thousand dollars.

(d(i)) Write this number in figures. [1]

(d(ii)) Write it in standard form. [1]

(e) A DVD costs \$2.75 to make and sells for \$8.20. Find the percentage profit. [3]

Kolyan buys water for \$2.60 and biscuits.

(a(i)) Cost of biscuits : cost of water = 3 : 2. Find the cost of biscuits. [2]

(a(ii)) He has \$9. Find the fraction spent on water and biscuits, in lowest terms. [2]

(a(iii)) The \$9 is 62.5% less than last week’s amount. Find last week’s amount. [3]

(b) A bicycle costs \$250 and loses 8% of its value each year. Find its value after 10 years, to the nearest dollar. [3]

A sale computer costs \$391, 15% below its original price. Find its original price. [3]

Kim’s mass falls from 63 kg to 61 kg during July. Find the percentage loss. [3]

(a) Papermill running costs of \$75246 are split labour : materials = 5 : 1. Find labour costs. [2]

(b) Profit rises from \$135890 in 2012 to \$150675 in 2013. Find the percentage increase. [3]

(c) The 2012 profit was 7% above 2011. Find the 2011 profit. [3]

Paper rolls have outer radius 30 cm, wooden core radius 2 cm and height 21 cm.

(d(i)) Find the volume of paper in one roll. [3]

(d(ii)(a)) Sheets are 21 cm by 29.7 cm and 0.125 mm thick. Convert the thickness to centimetres. [1]

(d(ii)(b)) Find the number of whole sheets cut from one roll. [4]

In July a supermarket sold 45981 bottles of fruit juice.

(a) Each bottle costs \$1.35. Find the total received, to the nearest hundred dollars. [2]

(b) July sales were 17% more than January sales. Find the January sales. [3]

(c) Apple : orange : cherry sales = 3 : 4 : 2. Find the number of orange bottles. [2]

(d) A bottle contains 1.5 litres. How many 330 ml glasses can be filled completely? [3]

(e) Five ninths of the bottles are recycled. How many is this? [2]

Compost has loam : sand : coir = 7 : 2 : 3.

(a(i)) Find the loam in 72 litres of compost. [2]

(a(ii)) A small bag has 13.5 litres of coir. Find its total compost volume. [2]

(a(iii)) A large bag costs \$8.40, an increase of 12% on last year. Find last year’s price. [3]

Teresa’s garden bed is a regular hexagonal prism: inside cross-section side 2 m; height 45 cm.

(b(i)) Show the cross-section area rounds to 10.4 m² to 3 significant figures. [3]

(b(ii)) Find the soil volume to fill it. [2]

(b(iii)) Soil is sold in one-tonne bags. 1 m³ has mass 1250 kg; 1 tonne = 1000 kg. Find the cost to fill the bed completely. [4]

Alfonso has \$75. Spending on music : films : books = 5 : 3 : 7; music costs \$16.50.

(a(i)) Find total spending on music, films and books. [3]

(a(ii)) Find this as a percentage of \$75. [1]

(b) Download times music : films : books = 2 : 9 : 1. Total is 3 h 33 min. Find the films’ time in h, min, s. [3]

(c) The music cost \$16.50 after a 12% reduction. Find its original cost. [3]

Theatre seats A : B : C = 11 : 8 : 7. Area B has 920 seats.

(a(i)) Show area C has 805 seats. [1]

(a(ii)) Give B as a percentage of all seats. [2]

(b) 80% of B tickets and 3/5 of C tickets sell. Total receipts are \$35834. Find the number of A tickets sold. [5]

(c) The receipts were 5% less than at the previous concert. Find the previous receipts. [3]

Pedro takes 84 minutes to do his homework. Pedro’s time : Eva’s time = 7 : 6. Find Eva’s time. [2]

A tennis club has 560 members, with men : women : children = 5 : 6 : 3.

(a(i)) Show there are 240 women. [2]

(a(ii)) Find the number of children. [1]

(b) \(5/8\) of the women play in a tournament. Find the number who do not. [2]

In 2013 each adult pays \$198 and each child \$75 annually.

(c(i)) Find the total membership fees. [2]

(c(ii)) The adult fee in 2013 is 5.6% more than in 2012. Find the 2012 fee. [3]

(d) The club buys 36 tennis balls for \$9.50 and sells them for \$0.75 each. Find the percentage profit. [3]

(e) A rectangular court has length 23.7 m and width 10.9 m, both to 1 decimal place. Find upper and lower bounds of its perimeter. [3]

Find 72 cents as a percentage of 83 cents. [1]

Find 17.5% of 44 kg. [2]

An arts festival ticket cost \$30 in 2012, 20% more than in 2011. Find the 2011 price. [3]

(a(i)) A camera magazine has 63 advert pages. Adverts : reviews = 7 : 5. Find the review pages. [2]

(a(ii)) In another issue, reviews and photographs occupy 56 pages. Reviews : photographs = 9 : 5. Find the photograph pages. [2]

(a(iii)) One copy costs \$4.90; an annual subscription of 13 copies costs \$48.80. Find the percentage discount. [3]

(b) In a car magazine, 25% of the pages sell second-hand cars. \(62\tfrac12\%\) of the remaining pages contain features; the other 36 pages are reviews. Find the total page count. [4]

The Tiger Sky Tower capsule holds 72 people. This was 75% of Singapore’s population in 1819. Find that population. [2]

Jamie needs 300 g of flour for 20 cakes. How much does he need for 12 cakes? [2]

Maria pays \$84 rent. It increases by 5%. Find her new rent. [2]

Bird food contains sunflower seed, millet and maize in the ratio 5:3:1.

(a(i)) Find the millet in 15 kg of bird food. [2]

(a(ii)) A small bag contains 60 g of sunflower seed. Find its total mass. [2]

(b) Sunflower seed costs \$204.50 for 30 kg from Jon or €96.40 for 20 kg from Ann. \$1 = €0.718. Which farm has the lower price per kilogram? Show working. [4]

(c) Bags fill at 420 g/s. How many complete 20 kg bags can be filled in 4 hours? [3]

(d) Brian sells each bag for \$15.30, making 12.5% profit. Find his cost per bag. [3]

(e) He orders 600 bags. Damage probability is 1/50. Find the expected damaged number. [1]

A concert hall has 1540 seats. Find the number of people when 55% of the seats are occupied. [1]

A school raises \$1380 in 2010 through a summer swim and winter walk, in the ratio summer:winter = 62:53.

(a)(i) Show that \$744 was raised in summer. [1]

(a)(ii) Alesha raises \$54.10. Express it as a percentage of \$744. [1]

(a)(iii) Bryan raises \$31.50 at 75 cents per pool length. Find the number of lengths. [2]

(b)(i) Students walk from A north to B, then on bearing 110° to C, then back to A. AB = BC. Find the bearing of A from C. [3]

(b)(ii) For seniors AB = BC = 6 km and the total walk is 18.9 km. Juniors walk 4 km north, then 4 km on bearing 110°, then return to A. Find their total distance. [3]

(c) The 2010 total is 8% less than in 2009. Find the 2009 total. [3]

Lucy earns \$277.20 in a week.

(a)(i) She spends one eighth on food. Find this amount. [1]

(a)(ii) She pays 15% in tax. Find this amount. [2]

(a)(iii) This week she earns 5% more than last week. Find her earnings last week. [3]

A shop sells 2200 coats. The ratio of men’s : women’s : children’s coats is 2 : 5 : 4.

(b)(i) Find the number of women’s coats. [2]

(b)(ii) The 2200 coats are \(44/73\) of all coats in stock. Find the original number in stock. [2]

Martha divides \$240 between spending and saving in the ratio 7 : 8. Find the spending amount. [2]

Maria increases her weekly homework time of 8 hours by 15%. Find the new time in hours and minutes. [3]

An athlete loses 2% of his mass during a marathon and finishes at 67.13 kg. Find his original mass. [3]

Abdullah and Jasmine buy a car for \$9000. Abdullah pays 45% and Jasmine pays the rest.

(a)(i) Find Jasmine’s payment. [2]

(a)(ii) Simplify the ratio Abdullah : Jasmine. [1]

(b) They share the annual running cost of \$2256 with Henri in the ratio Abdullah : Jasmine : Henri = 8 : 3 : 1. Find each payment. [3]

(c)(i) A truck costs \$15000 and loses 23% of its value each year. Find its value after 3 years. [3]

(c)(ii) Find the overall percentage loss after 3 years. [3]

Children go to camp.

(a)(i) Bananas cost \$0.85/kg. Fatima buys 20 kg at a 14% discount. Find the amount paid. [3]

(a)(ii) She pays \$16.40 for apples after an 18% discount. Find the original price. [3]

(a)(iii) The number of bananas : apples is 4 : 5. There are 108 bananas. Find the number of apples. [2]

(b) A tent costs \$c plus \$d per day. Hiring for 4 days costs \$27.10 and for 7 days \$34.30. Write and solve two equations in c and d. [4]

(c) The children travel 270 km, leaving 07:43 and arriving 15:13. Find the average speed. [3]

(d) \$540 was invested 2 years ago at 6% compound interest per year. Find the present amount. [2]

Amalie sells a shirt for \$21.60 at a profit of 20%. Find its cost price. [2]

A school has 220 boys and 280 girls.

(a) Find the ratio boys : girls in simplest form. [1]

(b) Students : teachers = 10 : 1. Find the number of teachers. [2]

(c) The committee has 21 students with boys : girls = 3 : 4. Find its number of girls. [2]

(d) 35% of the students each buy a disco ticket for \$1.60. Find the total ticket receipts. [3]

(e) This year the disco costs \$264, 10% more than last year. Find last year’s cost. [2]

In 2008, 3136 athletics tickets were sold, children : adults = 17 : 32.

(a)(i) Find the child-ticket count. [2]

(a)(ii) Child tickets cost \$2 and adult tickets \$4.50. Show that receipts were \$11392. [2]

(b) 2009 receipts were \$12748. Find the percentage increase from 2008. [3]

(c) 2008 receipts were 28% more than 2007. Find 2007 receipts. [3]

(a) Holiday costs Hansi : Megan = 7 : 4. Hansi pays \$756. Find Megan’s cost. [2]

Hansi earns \$7800 in 2008.

(b)(i) In 2009 he earns 15% more. Find the amount. [2]

(b)(ii) In 2010 he earns 10% more than 2009. Find the percentage increase from 2008 to 2010. [3]

(c) Megan earns \$9720 in 2009, 20% more than in 2008. Find her 2008 earnings. [3]

(d) Hansi invests \$500 at 4% yearly compound interest for 3 years. Find the final amount. [3]

Thomas,Ursula,Vanessa share \$200 in the ratio 3 : 2 : 5.

(a) Show Thomas receives \$60 and Ursula \$40. [2]

(b) Thomas buys a \$21 book. What percentage of his \$60 remains? [2]

(c) Ursula buys a game for \$36.80, 20% below its original price. Find that price. [3]

(d) Vanessa buys 5 books and 2 pencils for \$64.20. A book costs \$12 more than a pencil. Find a pencil’s price. [3]