In a 500 m long race, A beats B by 50m. While in a 1000 m long race B beats C by 200 m and in a race between C and D, which is 1200 m long, C beats D by 150 m. For the race between A and D, which is 500 m long, which of the following statements will be correct?

## Answer

Correct Answer : d ) A beats D by 185 m

Explanation :**Case 1: A Beats B by 50 m in a race of 500 m**

As, A beats B by 50 m so we can say that in the race, A covered complete 500 m race and in the same time B covers 500 – 50 = 450 m distance

Here, the ratio of distance covered by A and B to complete the race = 500 : 450 = 10 : 9

We know that when two persons travel their journey in equal amount of time at different speeds, then the ratio of the speed is equal to the ratio of the distance.

So, the ratio of speeds of A and B will be = 10 : 9 or 100 : 90 ….. (1)

**Case 2: B beats C by 200 m in a race of 1000 m**

As, B Beats C by 200 m so we can say that in the race, B covered complete 1000 m race and in the same time C covers 1000 – 200 = 800 m distance

Here, the ratio of distance covered by B and C to complete the race = 1000 : 800 = 5 : 4

We know that when two persons travel their journey in equal amount of time at different speeds, then the ratios of the speed is equal to the ratios of the distance.

So, the ratio of speeds of B and C will be = 5 : 4 or 90 : 72 ….. (2)

**Case 3: C beats D by 150 m in a 1200 m long race**

As, C beats D by 150 m so we can say that in the race, C covered complete 1200 m race and in the same time D covers 1200 – 150 = 1050 m distance

Here, the ratio of distance covered by C and D to complete the race = 1200 : 1050 = 8 : 7

We know that when two persons travel their journey in equal amount of time at different speeds, then the ratios of the speed is equal to the ratios of the distance.

So, the ratio of speeds of C and D will be = 8 : 7 or 72 : 63 ….. (3)

From equation 1, 2, and 3

Ratios of the speeds of A, B, C, and D= 100 : 90 : 72 : 63

Thus,

Ratio of speeds of A and D = 100 : 63

Ratio of distance covered by A and D in race = 100 : 63

Therefore, in a race of 500 m, A will beat D by a distance = 500 – 5 * 63 = 500 – 315 = 185 m

Hence, (d) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, etc.

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