Question : Three persons undertake to complete a piece of work for Rs. 1,200. The first person can complete the work in 8 days, the second person in 12 days and the third person in 16 days. They complete the work with the help of a fourth person in three days. What does the fourth person get?
Option 1: Rs. 180
Option 2: Rs. 200
Option 3: Rs. 225
Option 4: Rs. 250
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Correct Answer: Rs. 225
Solution :
Given: Three persons undertake to complete a piece of work for Rs. 1,200.
The first person can complete the work in 8 days, the second person in 12 days and the third person in 16 days.
First person's 1 day's work = $\frac{1}{8}$
Second person's 1 day's work = $\frac{1}{12}$
Third person's 1 day's work = $\frac{1}{16}$
They complete the work with the help of a fourth person in three days.
Their 1 day's work = $\frac{1}{3}$
Fourth person's 1 day's work = $\frac{1}{3}-\frac{1}{8}-\frac{1}{12}-\frac{1}{16}=\frac{1}{16}$
Ratio of their efficiency = $\frac{1}{8}:\frac{1}{12}:\frac{1}{16}:\frac{1}{16}=6:4:3:3$
$\therefore$ Fourth person's share = $\frac{3}{6+4+3+3}×1200=\frac{3}{16}×1200=$ Rs. 225
Hence, the correct answer is Rs. 225.
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