A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) is:

A. $35$

B. $36 \frac{2}{3}$

C. $37 \frac{1}{2}$

D. $40$

Correct Answer : D.

Let distance = x km and usual rate = y kmph.

T h e n, \frac{x}{y} - \frac{x}{y + 3} = \frac{40}{60} \Rightarrow 2 y (y + 3) = 9 x . . . . (i)

A n d, \frac{x}{y - 2} - \frac{x}{y} = \frac{40}{60} \Rightarrow y (y - 2) = 3 x . . . . (i i)

On dividing (i) by (ii), we get: x = 40.

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