Match List-I with List-II.
| List-I | List-II | ||
| (A) | Seconds by which A beats B in a 300 m race, if A runs at 6 m/s and B at 5 m/s | (I) | 5 |
| (B) | Speed of B (in m/s), if A beats B by 20 m or by 4 seconds | (II) | 10 |
| (C) | Metres by which A beats B in a 400 m race, if A runs at 8 m/s and B at 6 m/s | (III) | 30 |
| (D) | Start (in m) that A can give B in a 120 m race for a dead heat, if their speeds are in the ratio \(4 : 3\) | (IV) | 100 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(A) Seconds by which A beats B in a 300 m race, if A runs at 6 m/s and B at 5 m/s
This matches (II) 10. The lead in time is the difference of the finishing times:
\(300 \div 5 - 300 \div 6 = 60 - 50 = 10\) seconds
(B) Speed of B (in m/s), if A beats B by 20 m or by 4 seconds
This matches (I) 5. B runs the last 20 m in the extra 4 seconds:
\(20 \div 4 = 5\) m/s
(C) Metres by which A beats B in a 400 m race, if A runs at 8 m/s and B at 6 m/s
This matches (IV) 100. A finishes in \(400 \div 8 = 50\) seconds, and in that time B runs \(6 \times 50 = 300\) m:
\(400 - 300 = 100\) m
(D) Start (in m) that A can give B in a 120 m race for a dead heat, if their speeds are in the ratio \(4 : 3\)
This matches (III) 30. While A runs 120 m, B runs \(120 \times \frac{3}{4} = 90\) m:
\(120 - 90 = 30\) m