# Two persons undertake to do a piece of work for Rs. 1,200. One alone could do it in 6 days and the other in 8 days. With the assistance of a boy they

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Two persons undertake to do a piece of work for Rs. 1,200. One alone could do it in 6 days and the other in 8 days. With the assistance of a boy they finish it in 3 days. The difference between the shares of the two persons (in rupees) is
1. 150
2. 200
3. 250
4. 300

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Correct Answer - Option 1 : 150

Given:

First person can do a piece of work in 6 days

Second person can do a piece of work in 8 days

With the help of boy they together complete the work in 3 days

Calculation:

First person 1 day's work = 1/6

Second person 1 day's work = 1/8

Let boy's 1 day's work be 1/x

According to the question,

⇒ (1/6) + (1/8) + (1/x) = (1/3)

⇒ (1/x) = (1/3) - {(1/6) + (1/8)}

⇒ (1/x) = 1/24

∴ Ratio in shares of first person, second person and boys = (1/6) : (1/8) : (1/24)

⇒ Ratio in shares of first person, second person and boys = (1/6) × 24 : (1/28) × 24 : (1/24) × 24 = 4 : 3 : 1

The difference between shares of the two person = {(4 - 3)/(4 + 3 + 1)} × 1200 = 150

∴ The difference between shares of the two person is Rs. 150