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3 men and 4 women can complete a work in 12 days while 3 women and 4 boys can complete a work in 24 days.  Work done by 5 women is equal to work done by 10 boys. According to the amount of work done, one man is equivalent to how many boys?

3 men and 4 women can complete a work in 12 days while 3 women and 4 boys can complete a work in 24 days.  Work done by 5 women is equal to work done by 10 boys. According to the amount of work done, one man is equivalent to how many boys? Correct Answer 4

Given,

3 men and 4 women can complete a work in = 12 days

3 women and 4 boy can complete the same work in = 24 days

Work done by 5 women = work done by 10 men

Formula:

Total work = Efficiency × Time taken

Calculation:

Let efficiency of 1 man, 1 woman and 1 boy be x, y and z respectively

According to the question

⇒ (3x + 4y) × 12 = (3y + 4z) × 24      ----(1)

Also, 5y = 10z

⇒ z = y/2

From equation (1)

⇒ (3x + 8z) × 12 = (6z + 4z) × 24

⇒ (3x + 8z) = 10z × 2

⇒ 3x + 8z = 20z

⇒ 3x = 20z – 8z

⇒ 3x = 12z

⇒ x = 4z

∴ One man is equal to 4 boys.

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