# A man, 2 women and 4 boys can complete a piece of work in 15 days, 45 days and 18 days respectively. How many boys (to the nearest approximate whole n

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A man, 2 women and 4 boys can complete a piece of work in 15 days, 45 days and 18 days respectively. How many boys (to the nearest approximate whole number) must assist 5 men and 6 women so as to complete the work in 2 days?
1. 7
2. 8
3. 5
4. 6
5. None of these

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Correct Answer - Option 1 : 7

Given:

Time taken by a man to complete a work = 15 days

Time taken by 2 women to complete the work = 45 days

Time taken by 4 boys to complete the work = 18 days

Concept Used:

Efficiency = 1/Time taken

If "n" persons can complete the task in x days,

then 1 person can complete the same task in nx days.

Calculation:

Let the number of boys required for assisting be x

Time taken by a woman to complete the work = 45 × 2 = 90 days

Time taken by a boy to complete the work = 18 × 4 = 72 days

Hence, we can calculate the efficiency of 5 men, 6 women and x boys as:

⇒ (5/15) + (6/90) + (x/72) = (1/2)

⇒ (1/3) + (1/15) + (x/72) = (1/2)

⇒ (2/5) + (x/72) = (1/2)

⇒ x/72 = (1/2) – (2/5)

⇒ x = 7.2

∴ The required number of boys is approximately 7