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Clock Angle Rate of Change

CAT 2023 Slot 1 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2023 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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The minor angle between the hours hand and minutes hand of a clock was observed at 8:48 am. The minimum duration, in minutes, after 8.48 am when this angle increases by 50% is

  1. A.

    36/11

  2. B.

    24/11

  3. C.

    2

  4. D.

    4

Answer

B

Explanation

At 8:48 am:

  • Position of minute hand =48×6∘=288∘= 48 \times 6^\circ = 288^\circ
  • Position of hour hand =8×30∘+48×0.5∘=240∘+24∘=264∘= 8 \times 30^\circ + 48 \times 0.5^\circ = 240^\circ + 24^\circ = 264^\circ
  • Minor angle between them =288∘−264∘=24∘= 288^\circ - 264^\circ = 24^\circ.

An increase of 50% means the new angle becomes 24∘×1.5=36∘24^\circ \times 1.5 = 36^\circ. So the angle needs to increase by 12∘12^\circ.

Relative speed of minute hand with respect to hour hand =6∘−0.5∘=5.5∘=112∘= 6^\circ - 0.5^\circ = 5.5^\circ = \frac{11}{2}^\circ per minute.

Time required =1211/2=2411= \frac{12}{11/2} = \frac{24}{11} minutes.

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