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Leaving home at the same time | Quantitative Aptitude - CAT TSD

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The question below is from previous year CAT question from CAT 2020 exam comes from CAT Time Speed Distance: 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? 

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2020 - Slot 1 - Quantitative Aptitude - TSD - Question 19 - Leaving home at the same time

Q.19: 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. 12
2. 11
3. 13
4. 14

Correct Answer: 12

Speed are 8 km/hr and 15 km/hr

So it takes 15t times and 8t times

Difference of times = 15t – 8t = 7t

7t = 35 minutes (10:15 min – 9:40 min)

t = 5 minutes

He takes 75 minutes by travelling at 8 km/hr and 40 minutes if travelled at 15 km/hr

He starts at 9 am.

So, 9:10 to 10:00 = 50 minutes

15 km/hr = 40 min

And at what speed he should travel, so as to reach there within 50 minutes

15×40 / 50  = 12 km/hr

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