CAT 2017 Set-1 | Question: 70

Question

A man leaves his home and walks at a speed of $12$ km per hour, reaching the railway station $10$ minutes after the train had departed. If instead he had walked at a speed of $15$ km per hour, he would have reached the station $10$ minutes before the train's departure. The distance (in km) from his home to the railway station is

• A. $15$
• B. $16$
• C. $17$
• D. None of these

Answer 1

Let the distance (home to the railway station), be $D$ km.

We know that, $\text{Time} = \dfrac{\text{Distance}}{\text{Speed}}$

According to the question, $\frac{D}{12} – \frac{D}{15} = \frac{20}{60}$

$\Rightarrow \frac{5D – 4D}{60} = \frac{20}{60}$

$\Rightarrow D = 20$ km

$\therefore$ Distance from home to the railway station $= 20$ km.

Correct Answer $:\text{D}$