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A man reaches his office 30 minutes too late if he walks from his home at 3 km an hour and reaches 40 minutes too early if he walks at 4 km an hour. How far is his office from his house?

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7 km

14 km

5 km

3 km

answer is B.

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Detailed Solution

Given,
Suppose distance between his office and home= x km
We know that,

speed = \frac{distance}{time}

So,

time = \frac{distance}{speed}

The time taken by the man to reach the office if he walks at a speed of 3 kmph

-30 = \frac{x}{3} \dots \dots \dots (1) (negative sign used for late of 30 \min)

Now he reaches 40 min early with 4 km/hr

40 = \frac{x}{4} \dots \dots \dots (2)

\frac{x}{4} = 40

min earlier
Now, subtract equation (ii) from equation (i).

\begin{matrix} \frac{x}{3} - \frac{x}{4} = 40 - (- 30) \min \\ \frac{x}{3} - \frac{x}{4} = 70 \min \end{matrix}

\begin{matrix} \frac{x}{3} - \frac{x}{4} = \frac{70}{60} (since, 1 hr = 60 \min) \\ \frac{4 x - 3 x}{12} = \frac{70}{60} \\ \frac{x}{12} = \frac{70}{60} \\ x = \frac{70 \times 12}{60} \\ x = 14 km \end{matrix}

So, the distance of his office from house = 14 km.
So, option 2 is the correct answer.

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