Question : In a linear race of 500 m, A can beat B by 50 m, and in a race of 600 m, B can beat C by 60 m. By how many metres will A beat C in a race of 400 m?
Option 1: 70
Option 2: 68
Option 3: 76
Option 4: 72
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Correct Answer: 76
Solution :
A can beat B by 50 m in a race of 500 m.
If A is at 500 m, then
B = 500 – 50 = 450 m
So, A: B = 500: 450 = 10: 9 = 100: 90 ---------(i)
B can beat C by 60 m in a race of 600 m.
If B is at 600 m, then
C = 600 – 60 = 540 m
B: C = 600: 540 = 10: 9 = 90: 81 -----------(ii)
⇒ A: B: C = 100: 90: 81
In a 400 m race, when A is at 400 m,
B = 90 × 4 = 360 m
C = 81 × 4 = 324 m
A will beat C by (400 – 324) = 76 m
Hence, the correct answer is 76.
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