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### Question

Two trains running in opposite directions cross each other in 31 seconds. They, respectively, take 14 and 42 seconds to cross a man standing on the platform. What is the ratio of their speeds?

**A**

$1{6/11}$.

**B**

$2{4/5}$.

**C**

${6/13}$.

**D**

$3{11/13}$.

**Soln.**

**Ans: a**

Let the ratio of their speeds by r. If the speed of one train is v, then the speed of the other is rv. By the speed and distance formula, the sum of their lengths is $(v × 14) + (rv × 42)$ which should equal the value obtained from the time they take to cross each other,i.e., $(v + rv) × 31)$. So $v × (14 + r × 42$ = $v × (1 + r) × 31).$ Cancelling v and solving for r we get ${17/11}$.