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CAT 2017 Slot 2 — QA Question 2

Linear RaceEasy

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 & solution

Correct answer: 1900

Answer: 1900

Solution

Easy

Each runner has a constant speed, so distances covered in the same time are in the ratio of speeds. Get the speed ratio A:B:CA:B:C, then scale CC's distance to the moment AA finishes 1010 km.

1

Speed ratios from the "beats by" data. When AA runs 1010 km, BB runs 99 km; when BB runs 1010 km, CC runs 99 km.

A:B=10:9B:C=10:9\begin{aligned} &A:B=10:9\\ &B:C=10:9 \end{aligned}
2

Combine into one ratio. Make BB common by scaling each ratio (LCM of the BB-terms).

A:B=100:90B:C=90:81⇒ A:B:C=100:90:81(common B=90)\begin{aligned} &A:B=100:90\\ &B:C=90:81\\ &\Rightarrow\ A:B:C=100:90:81 \quad\text{(common }B=90) \end{aligned}
3

Distance CC covers when AA finishes. When AA runs the full 1000010000 m, CC covers 81100\tfrac{81}{100} of that.

C=81100×10000=8100 m⇒ gap=10000−8100=1900 m\begin{aligned} &C=\frac{81}{100}\times 10000=8100\ \text{m}\\ &\Rightarrow\ \text{gap}=10000-8100=1900\ \text{m} \end{aligned}
A beats C by 1900 mA\text{ beats }C\text{ by }1900\ \text{m}

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CAT 2017 Slot 2 QA Q2: In a 10 km race, A, B and C, each running at uniform speed, get the gold, silver, and bronze medals, respectiv — Solution | TheCATExam