Question

By walking at \(\dfrac{4}{5}\) of his usual speed, a man reaches office 10 minutes later than usual. What is his usual time?

• A. 20 min
• B. 40 min
• C. 30 min
• D. 50 min

Hint:

If speed drops to 4/5, time rises to 5/4 of usual; the 1/4 extra equals the given 10-minute delay.

Answer 1

The Correct Option is B

Instead of algebra, this can be solved by picking convenient numbers for speed and time that respect the inverse relationship.

1. Let the usual speed be 5 units and usual time be 4 units, so usual distance $= 5 \times 4 = 20$ units (a fixed constant).
2. New speed is $\frac{4}{5}$ of usual, so new speed $= 4$ units.
3. New time $= \frac{\text{distance}}{\text{new speed}} = \frac{20}{4} = 5$ units.
4. The delay is $5 - 4 = 1$ unit of time, and this equals the given 10 minutes, so 1 unit $= 10$ minutes.

Usual time was 4 units $= 4 \times 10 = 40$ minutes.

The correct answer is option B.