In a kilometer race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 m, then
Match List-I with List-II
| List-I | List-II | ||
| (A) | Time taken by A to run 1 km | (I) | 250 seconds |
| (B) | Time taken by B to run 1 km | (II) | 45 seconds |
| (C) | Time taken by C to run 1 km | (III) | 235 seconds |
| (D) | A beats C by | (IV) | 205 seconds |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (IV), (B) - (III), (C) - (I), (D) - (II)
A finishes 30 seconds before B, and B finishes 15 seconds before C, so A finishes 30 + 15 = 45 seconds before C.
A also beats C by 180 m: when A finishes, C still has 180 m to run, and C takes 45 seconds to cover it. This gives the speed of C:
\( \displaystyle \text{Speed of C}=\frac{180}{45}=4 \text{ m/s} \)
\( \displaystyle \text{Time of C for 1 km}=\frac{1000}{4}=250 \text{ s} \)
\( \displaystyle \text{Time of B}=250-15=235 \text{ s} \)
\( \displaystyle \text{Time of A}=235-30=205 \text{ s} \)
(A) Time taken by A to run 1 km
This matches (IV) 205 seconds.
(B) Time taken by B to run 1 km
This matches (III) 235 seconds.
(C) Time taken by C to run 1 km
This matches (I) 250 seconds.
(D) A beats C by
This matches (II) 45 seconds.
So the matching is (A)-(IV), (B)-(III), (C)-(I), (D)-(II).