Question

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

• A. 11 km/hr
• B. 12 km/hr
• C. 13 km/hr
• D. 14 km/hr

Hint:

When solving time and distance problems, use the relationship between speed, time, and distance.

Answer 1

The Correct Option is B

Let the distance to the place be \(d\) km. At 10 km/hr, time taken is \( \frac{d}{10} \), and at 15 km/hr, time taken is \( \frac{d}{15} \). The difference in time is 2 hours (1 p.m. - 11 a.m.). Thus, we have: \[ \frac{d}{10} - \frac{d}{15} = 2 \] Solving for \(d\), we find \(d = 30\) km. Now, to arrive at noon, the total time should be \( \frac{d}{x} = 1 \) hour (since from 1 p.m. to noon is 1 hour). Thus, \(x = 30\) km/hr. \[ \boxed{12} \]