• # question_answer A man covers a certain distances between his house and office on scooter. With an average speed of 30 km/hr, he is late by 10 min., however, with a speed 40 km/hr, he reaches his office 5 min earlier. Find the distance between his house and the office. A)  20 km             B)  10 kmC)  15 km             D)  30 km

Let distance be $x$ km. Time taken to cover $x$ km at 30 km/hr. $=\frac{x}{30}hrs$ Time taken to cover x km at 40 km/hr. $=\frac{x}{40}hrs$ Difference between the time taken $=15\min =\frac{1}{4}hr$ $\therefore \frac{x}{30}-\frac{x}{40}=\frac{1}{4}$ $\frac{40x-30x}{1200}=\frac{1}{4}$ $\frac{10x}{1200}=\frac{1}{4}$ $x=\frac{1200}{4\times 10}=30$