CAT 2020 Question Paper | Quants Slot 3

This question is from Speed time distance. Questions from Speed time distance have appeared in every edition of the CAT Exam. This is a very interesting topic as it can be relatable in real-life scenarios too. If you're in a hurry, then solve this question. This question might help you to calculate how late you're going to be. To explore 1000+ intriguing questions, check out 2IIM CAT Question Bank, and give your CAT Preparation the right direction.

Question 22 : Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

Video Explanation

Explanatory Answer

Vimala's speed has decreased from 40kmph to 35 kmph. That means her current speed is $\frac{35}{40}$ of the original Speed. That means, her current speed is $\frac{7}{8}$ th of the original speed. Therefore, the time taken will be $\frac{8}{7}$ th of the original time taken.

Since she is 6 minutes late when travelling at 35kmph, $\frac{1}{7}$th of the original time taken is 6 minutes.
Therefore the total time taken originally is 7 × 6 = 42 minutes.

$\frac{1}{3}$ rd of the original time taken = $\frac{42}{3}$ = 14 minutes.
$\frac{1}{3}$ rd of the total distance is generally covered in 14 minutes.
Currently the same distance is to be covered in (42 - 14 - 8 = 20) minutes.

So, to reach the Destination on time, Vimala, must cover the same $\frac{1}{3}$ rd of the Distance in 20 minutes instead of 14 minutes.
That means she has to $\frac{20}{14}$ of the initial time.
Which is $\frac{10}{7}$ of the original time
This implies that, in order to reach at the same point of time. The speed had to $\frac{7}{10}$ or 70% of the original speed.

So, she has to travel at 70% of 40kmph = 28kmph.

The answer is, "28"

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