Multiple choice

Directions: Study the following information carefully and answer the question that follows. A man walking at the speed of 7 km/hr arrives at a certain place in 18 days. He takes rest for 8 hours per day during the journey. Now he has to take another journey which is thrice as long as the previous one. If he has to cover the distance in 35 days only with a speed of 8 km/hr, for how much time should he take rest every day during his journey?

  1. 12 hours

  2. 8 hours

  3. 4.2 hours

  4. 2.4 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Distance 1 = 7 km/hr * (18 days * 24 hours - 18 * 8 hours) = 7 * (432 - 144) = 7 * 288 = 2016 km. Distance 2 = 3 * 2016 = 6048 km. Total hours available = 35 * 24 = 840 hours. Walking time = 6048 / 8 = 756 hours. Rest time = 840 - 756 = 84 hours. Rest per day = 84 / 35 = 2.4 hours.

AI explanation

In the first journey the man walks for 16 hours each day after taking 8 hours of rest, so the total walking time is 18 times 16 which is 288 hours. Using the formula Distance equals Speed multiplied by Time, the first distance is 7 km/hr times 288 hours which equals 2016 km. The second journey is three times as long, making it 3 times 2016 which equals 6048 km. At a speed of 8 km/hr the walking time needed is 6048 divided by 8 which equals 756 hours. Spread over 35 days he walks for 756 divided by 35 which is 21.6 hours per day, leaving 24 minus 21.6 which equals 2.4 hours for rest. The answer is 2.4 hours.

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