A man cycles at the speed of 8km hr and reaches office at 11 am and when he cycles at the speed of 1...........

Quantitative Aptitude (CPO) Time & distance

A man cycles at the speed of 8km/hr and reaches office at 11 am and when he cycles at the speed of 12 km/hr he reaches office at 9 am. At what speed should he cycle so that he reaches his office at 10 am?

9.6 km/hr

10 km/hr

11.2 km/hr

Cannot be determined

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Explanation:

- Cycling at 8 km/hr: The man reaches the office at 11 am.

- Cycling at 12 km/hr: He reaches the office at 9 am.

- Time difference: The difference in time between the two speeds is 2 hours.

- Distance calculation: Let \( D \) be the distance from home to office. Using the formula \( \text{Distance} = \text{Speed} \times \text{Time} \), you can find \( D = 8 \times t_1 \) and \( D = 12 \times t_2 \).

- Equation for time difference: Since \( t_1 - t_2 = 2 \), \( \frac{D}{8} - \frac{D}{12} = 2 \).

- Solve for D: Simplifying gives \( D = 48 \) km.

- Desired arrival at 10 am: The man wants to reach an hour later than 9 am.

- Time calculation for desired speed: Time needed = 1 hour, Speed needed = \( \frac{48}{1 + 1} \).

- Correct speed: Calculate \( = \frac{48}{2} = 9.6 \text{ km/hr} \).

- Chosen option: This matches option 1.

- Correct Answer: Option 1 - 9.6 km/hr