Ram, while going to school, reduces his speed to 4/5th of his actual speed and reaches 15 minutes late. Find the actual time of R…

Question

Ram, while going to school, reduces his speed to 4/5th of his actual speed and reaches 15 minutes late. Find the actual time of Ram.

1. A. 45 minutes
2. B. 60 minutes (Correct answer)
3. C. 30 minutes
4. D. 75 minutes

Correct Answer

Option B — B

Detailed Solution & Explanation

The correct answer is Option B.

Key Points

• When speed becomes 4/5 of usual, time becomes the reciprocal, 5/4 of usual (speed and time are inversely proportional for a fixed distance).
• Extra time = 5/4·T − T = T/4, and this equals the 15-minute delay:
• T/4 = 15 → T = 60 minutes.
• So Ram's actual (usual) time is 60 minutes.

Exam Tip

• if speed becomes a/b of normal, time becomes b/a of normal; the extra time = (b/a − 1)·usual time.
• Set it equal to the given delay and solve.

Additional Information

• Speed and time are inversely proportional over a fixed distance: at 4/5 speed, time becomes 5/4 of usual, so the extra 1/4 of the usual time equals the 15-minute delay.
• Usual time is therefore 60 minutes.
• The general result: if speed becomes a/b of usual, the extra time is (b − a)/a of the usual time — worth memorising for this very common question type.