Question : A man, a woman, and a boy can complete a job in 3, 5, and 15 days, respectively. How many boys must assist 1 man and 1 woman to complete the job in $\frac{1}{5}$ of a day?
Option 1: 67
Option 2: 35
Option 3: 56
Option 4: 47
Correct Answer: 67
Solution :
Man can complete work in 3 days.
Women can complete work in 5 days.
Boy can complete work in 15 days.
LCM of 3, 5, and 15 is 15
Total work = 15 units
Efficiency of a man = $\frac{15}{3}$ = 5 units
Efficiency of a woman = $\frac{15}{5}$ = 3 units
Efficiency of a boy = $\frac{15}{15}$ = 1 units
To complete the whole work in 1 day, the effective efficiency must be 15
$\therefore$ To complete the whole work in $\frac{1}{5}$ day, efficiency should be 75.
The effective efficiency of man and woman = (5 + 3) = 8 units.
The remaining work can be done by the number of boys with the efficiency of 1 =(75 – 8) = 67.
Hence, the correct answer is 67.
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