A man covers a certain distance on scooter. Had he moved

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A man covers a certain distance on scooter. Had he moved 3 km/h faster, he would have taken 40 min less. If he had moved 2 km/ slower, he would have taken 40 min more. The distance (in
km) is ?

1. 42.5
2. 36
3. 37.5
4. 40

Correct Option: D

Let distance and original speed of the man be d km and s km/h.
Then,
d/s - d/s + 3 = 2/3
⇒ [d(s + 3 - s)]/[s(s + 3)] = 2/3
⇒ 9d = 2s(s + 3) ...(i)

And d/(s - 2) - d/s = 2/3
⇒ [d(s - s + 2)]/[s(s - 2)] = 2/3
⇒ 3d = s(s - 2) ...(ii)

From Eqs.(i) and (ii), we get
3s(s - 2) = 2s(s + 3)
⇒ 3s² - 6s = 2s² + 6s
⇒ s² = 12s
⇒ s = 12

From Eq.(ii), we get
3d = 12(12 - 2)
∴ d = 40 km