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Amal's speed to reach office

CAT 2020 Slot 1 · Quantitative Ability · Medium · Time, Speed & Distance

This is a medium Quantitative Ability question from the CAT 2020 Slot 1 paper. It tests Time, Speed & Distance. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Leaving home at the same time, Amal reaches office at 10:15 am if he travels at 8kmph, and at 9:40 am if he travels at 15kmph. Leaving home at 9:10 am, at what speed, in kmph, must he travel so as to reach office exactly at 10:00 am?

  1. A.

    12

  2. B.

    11

  3. C.

    13

  4. D.

    14

Answer

A

Explanation

Time difference between 10:15 am and 9:40 am is 35 minutes =3560= \frac{35}{60} hours.

Let distance to office be dd km. d8−d15=3560  ⟹  7d120=3560  ⟹  d=10 km\frac{d}{8} - \frac{d}{15} = \frac{35}{60} \implies \frac{7d}{120} = \frac{35}{60} \implies d = 10\text{ km}

Time taken at 8 kmph =108=1.25 hours=75 minutes= \frac{10}{8} = 1.25\text{ hours} = 75\text{ minutes}. Since he reaches at 10:15 am, he leaves home at 10:15−75 min=9:00 am10:15 - 75\text{ min} = 9:00\text{ am}.

If he leaves home at 9:10 am and must reach by 10:00 am:

  • Time available =50 minutes=56 hours= 50\text{ minutes} = \frac{5}{6}\text{ hours}.
  • Required speed =105/6=12 kmph= \frac{10}{5/6} = 12\text{ kmph}.

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