Question 110

# Shruti and Krishna left Delhi for Noida at the same time. While Shruti was driving her car, Krishna, an environmentalist by profession, was traveling on his bicycle. Having reached Noida, Shruti turned back and met Krishna an hour after they started. Krishna continued his journey to Noida after the meeting, while Shruti turned back and also headed for Noida. Having reached Noida, Shruti again turned back and met Krishna 30 minutes after their first meeting. The time taken by Krishna to cover the distance between Delhi and Noida is

Solution

Let the distance between Delhi and Noida is X km and Krishna's speed is d km/hr.

When they met for the first time, Distance covered by Krishna = d km

Distance covered by Shruti = 2X-d km

So the ratio of speeds of Shruti and Krishna is 2X - d : d                                                  ...(1)

Between 1st and 2nd meeting,   Distance covered by Krishna = d/2 km

So distance covered by Shruti will be  = (X-d)+(X-3d/2)= 2X-5d/2

So the ratio of speeds of Shruti and Krishna in this case will be 2X-5d/2 : d/2                  ...(2)

By equating (1) and (2)

$$\frac{2X - d}{d}$$  =  $$\frac{2X-5\frac{d}{2}}{\frac{d}{2}}$$

$$X=2d$$

Therefore the distance between Delhi and Noida is 2d and Krishna will take 2 hours to cover that distance with speed of d km/hr.

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