Multiple choice

In a Bilaspur village, 12 men and 18 boys completed construction of a primary health centre in 60 days, by working for 7.5 hours a day. Subsequently, the residents of the neighbouring Harigarh village also decided to construct a primary health centre in their locality, which would be twice the size of the centre built in Bilaspur. If a man is able to perform the work equal to the same done by 2 boys, then how many boys will be needed to help 21 men to complete the work in Harigarh village in 50 days, working for 9 hours a day?

  1. 45

  2. 48

  3. 40

  4. 42
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work = Men * Days * Hours. 1 man = 2 boys. 12 men + 18 boys = 24 boys + 18 boys = 42 boys. Work1 = 42 * 60 * 7.5 = 18900 boy-hours. Work2 = 2 * Work1 = 37800 boy-hours. 21 men + x boys = 42 boys + x boys = (42+x) boys. Work2 = (42+x) * 50 * 9 = 37800. 42+x = 37800 / 450 = 84. x = 42.

AI explanation

Using the man-hour equivalence method, the total work in Bilaspur is (12 men plus 18 boys) times 60 days times 7.5 hours per day. Since 1 man equals 2 boys, the 12 men equal 24 boys, making the team 42 boys, so the total work is 42 boys times 450 hours, or 18900 boy-hours. The Harigarh project is twice this size, totaling 37800 boy-hours. The target team of 21 men equals 42 boys, and they need to work 50 days times 9 hours per day, equaling 450 hours, which yields a total capacity of 42 boys times 450 hours, or 18900 boy-hours. The remaining work is 18900 boy-hours, which divided by the 450 working hours means 42 additional boys are needed.

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