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Two Boats Approaching Each Other

CAT 2004 Slot 1 · Quantitative Ability · Easy · Speed Time Distance

This is an easy Quantitative Ability question from the CAT 2004 Slot 1 paper. It tests Speed Time Distance. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Two boats, traveling at 5 km/hr5\text{ km/hr} and 10 km/hr10\text{ km/hr}, head directly towards each other. They begin at a distance of 20 km20\text{ km} from each other. How far apart are they (in km) one minute before they collide?

  1. A.

    112\frac{1}{12}

  2. B.

    16\frac{1}{6}

  3. C.

    14\frac{1}{4}

  4. D.

    13\frac{1}{3}

Answer

C

Explanation

Relative speed of the two boats =5+10=15 km/hr= 5 + 10 = 15\text{ km/hr}. In 1 minute1\text{ minute} (1/60 hour1/60\text{ hour}), the distance covered by both boats together is: Distance=15×160=14 km\text{Distance} = 15 \times \frac{1}{60} = \frac{1}{4}\text{ km} Thus, one minute before collision, they are 14 km\frac{1}{4}\text{ km} apart.

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