CAT 2020 Question Paper | Quants Slot 2

Worried about your CAT preparation online? Not sure where to start your preparation from? Stressed out about the direction you should steer your CAT Preparation in? Say goodbye to all your worries! One of the best ways to begin your preparation is practicing the CAT previous year paper. This will help you to get an idea about what the CAT Question Paper might throw at you. Start with this question from the topic Races of the Quantitative Ability section of the CAT exam and consistently take your preparation onwards and upwards.

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

Video Explanation

Explanatory Answer

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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