# CAT 2020 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Quants Questions | Question 1

Question 1 : In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

1. 550
2. 475
3. 500
4. 450

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Let the length of the race track be 'x' km.

By the time A finishes the race, B lags by 45km.
That is, in the same time, while A runs x kms, B runs (x-45) kms
Ratio of Speeds of A and B = $$frac{x}{x-45}$ By the time B finishes the race, C lags by 50km. That is, in the same time, while B runs x kms, C runs$x-50) kms
Ratio of Speeds of B and C = $$frac{x}{x-50}$ By the time A finishes the race, C lags by 90km. That is, in the same time, while A runs x kms, C runs$x-90) kms
Ratio of Speeds of A and C = $$frac{x}{x-90}$$Ratio of Speeds of A and B) × (Ratio of Speeds of B and C) = (Ratio of Speeds of A and C)
$$frac{x}{x-45}$ × $\frac{x}{x-50}$ = $\frac{x}{x-90}$ $\frac{x}{x-45}$ = $\frac{x-50}{x-90}$ If $\frac{a}{b}$ = $\frac{c}{d}$; then $\frac{a}{b}$ = $\frac{c-a}{d-b}$ Threfore, $\frac{x}{x-45}$ = $\frac{x-50 - x}{x-90 -$x-45$})
$$frac{x}{x-45}$ = $\frac{-50}{-45}$ = $\frac{10}{9}$ $\frac{x}{x-45}$ = $\frac{10}{9}$ 9x = 10x - 450 x = 450. or Ratio of Speeds of A and B = $\frac{10}{9}$ By the A covers x, B covers 0.9x Since A beats B by 45km, 0.1x = 45 x = 450. The question is "In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance$in km) over which the race has been conducted is"

##### Hence, the answer is, "450"

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