CAT 2023 Slot 1 · Quant · Question 9

Measure both hands as angles clockwise from the 12 mark.

The minute hand moves {6}^{∘} per minute, so at 48 minutes past it stands at 48\times 6={288}^{∘}.

The hour hand moves {0.5}^{∘} per minute, so at 8:48 it stands at 8\times 30+48\times 0.5=240+24={264}^{∘}.

The gap between them is 288-264={24}^{∘}, which is already the minor angle.

Increasing it by 50% means reaching 24\times 1.5={36}^{∘}.

The minute hand gains on the hour hand at 6-0.5={5.5}^{∘} per minute.

The minute hand is currently ahead, so the gap simply widens at that rate.

Letting t be the minutes needed, 24+5.5t=36.

So 5.5t=12, giving t=\frac{12}{5.5}=\frac{24}{11} minutes — the second option.

Shortcut. The relative speed \frac{11}{2} degrees per minute puts an 11 in every denominator, which already points at the answer's shape. The extra {12}^{∘} needed divided by \frac{11}{2} is \frac{24}{11}, and the alternative — waiting for the hands to close and reopen — takes far longer, so it is not the minimum.