2015 · Q24
In a race A, B and C take part. A beats B by 30 m, B beats C by 20 m and A beats C by 48 m. Which of the following is/are correct ?
- 1The length of the race is 300 m.
- 2The speeds of A, B and C are in the ratio 50 : 45 : 42.
Select the correct answer using the code given below:
Elementary MathematicsTime and Work
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Let the race be L m. Then vB/vA = (L - 30)/L, vC/vB = (L - 20)/L and vC/vA = (L - 48)/L; consistency gives (L - 30)(L - 20) = L(L - 48), i.e. L = 300, so statement 1 is correct. The speeds are in ratio 300:270:252 = 50:45:42, so statement 2 is correct. Hence option (c).