(a) To find the interquartile range (IQR), we need to determine the values of the lower quartile (\(Q_1\)) and the upper quartile (\(Q_3\)).

\(Q_1\) is at the 25th percentile, which corresponds to \(0.25 \times 120 = 30\) on the cumulative frequency axis. From the graph, \(Q_1 \approx 23.7\) seconds.

\(Q_3\) is at the 75th percentile, which corresponds to \(0.75 \times 120 = 90\) on the cumulative frequency axis. From the graph, \(Q_3 \approx 31\) seconds.

Thus, the interquartile range is \(Q_3 - Q_1 = 31 - 23.7 = 7.3\) seconds.

(b) To find \(T\), note that 35% of the children took longer than \(T\) seconds. This means 65% took \(T\) seconds or less.

65% of 120 children is \(0.65 \times 120 = 78\).

From the graph, the time corresponding to a cumulative frequency of 78 is approximately \(28.5\) seconds.