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Walking 3/4 his normal speed, Rabi is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office:

A. 48 min. B. 60 min. C. 42 min. D. 62 min. Answer: Option A
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Solution(By Apex Team)

1st method: $\frac{4}{3}$ of usual time = Usual time + 16 minutes; Hence, $\frac{1}{3}$rd of usual time = 16 minutes; Thus, Usual time = 16 × 3 = 48 minutes.

Explanation

We can let r = Rabi’s normal speed and t = the time he normally takes to reach his office from home. Thus, the distance between his home and his office is rt. Since we are given that he is 16 minutes late in reaching his office when he walks at 3/4 of his normal speed. we can say that his new speed = (3/4)r and his new time = t + 16. Thus, the distance between his home and his office, in terms of the new speed and new time, is (3/4)r(t + 16). Since the distance between his home and his office doesn’t change in relation to speed and time, we have: rt = (3/4)r(t + 16) Divide both sides by r, we have: t = (3/4)t + 12 (1/4)t = 12 t = 48 Min.

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