Multiple choice

A man wants to reach a certain destination. One-sixth of the total distance is muddy while half the distance is tar road. For the remaining distance he takes a boat. His speed of travelling in mud, in water, on tar road is in the ration $3 : 4 : 5$. The ratio of the duration he requires to cross the patch of mud, stream and tar road is

  1. $\dfrac { 1 }{ 2 } : \dfrac { 4 }{ 3 } : \dfrac { 5 }{ 2 } $
  2. $3 : 8 : 15$
  3. $10 : 15 : 18$
  4. $1 : 2 : 3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a total distance D, the mud, water, and tar distances are D/6, D/3, and D/2. Dividing each distance by its speed ratio 3:4:5 gives times proportional to D/18, D/12, and D/10, which simplify to 10:15:18.

AI explanation

Assuming the total distance is 6 units, the distances for the mud, tar road, and water are 1, 3, and 2 units respectively. The speeds for mud, water, and tar road are in the ratio 3:4:5, so let the speeds be 3k, 4k, and 5k. The time required for each patch is distance divided by speed: mud takes 1/3k, water takes 2/4k, and the tar road takes 3/5k. Finding a common denominator of 60k, the times become 20/60k for mud, 30/60k for water, and 36/60k for the tar road. The ratio of these durations is 20:30:36, which simplifies to 10:15:18.

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