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Select the correct answerA man starts from a place P and reaches the place Q in 7 hours. He travels 1/4th of the distance at 10 km/hour and the remaining distance at 12 km/hour.The distance between P and Q is?Options72 km80 km70 km90 km

Question

Select the correct answerA man starts from a place P and reaches the place Q in 7 hours. He travels 1/4th of the distance at 10 km/hour and the remaining distance at 12 km/hour.The distance between P and Q is?Options72 km80 km70 km90 km

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Solution

Let's solve this step by step:

  1. Let's assume the total distance between P and Q is D km.

  2. According to the problem, the man travels 1/4th of the distance at 10 km/hour and the remaining distance at 12 km/hour.

  3. So, the distance traveled at 10 km/hour = D/4 km and the distance traveled at 12 km/hour = D - D/4 = 3D/4 km.

  4. The total time taken is the sum of the time taken at 10 km/hour and the time taken at 12 km/hour, which is given as 7 hours.

  5. Time = Distance/Speed. So, the time taken at 10 km/hour = (D/4)/10 = D/40 hours and the time taken at 12 km/hour = (3D/4)/12 = D/16 hours.

  6. Therefore, D/40 + D/16 = 7. To solve for D, you need to find a common denominator for 40 and 16, which is 160.

  7. So, 4D/160 + 10D/160 = 7, which simplifies to 14D/160 = 7.

  8. Solving for D gives D = 7 * 160 / 14 = 80 km.

So, the distance between P and Q is 80 km.

This problem has been solved

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