10 km Race Medals Comparison

CAT 2017 Slot 2 · QA · Easy · Races

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In a 10 km race, A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?

Answer

1900

Explanation

When A covers 10 km, B covers 10−1=910 - 1 = 9 km. So, Speed of ASpeed of B=109\frac{\text{Speed of A}}{\text{Speed of B}} = \frac{10}{9}.

When B covers 10 km, C covers 10−1=910 - 1 = 9 km. So, Speed of BSpeed of C=109\frac{\text{Speed of B}}{\text{Speed of C}} = \frac{10}{9}.

Therefore, Speed of ASpeed of C=109×109=10081\frac{\text{Speed of A}}{\text{Speed of C}} = \frac{10}{9} \times \frac{10}{9} = \frac{100}{81}.

When A covers 10 km (10,000 metres), the distance covered by C is: Distance of C=10000×81100=8100 metres\text{Distance of C} = 10000 \times \frac{81}{100} = 8100\text{ metres}

Hence, A beats C by 10000−8100=190010000 - 8100 = 1900 metres.

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