Question : 5 men and 8 women can complete a work in 12 days working together, while 3 men and 7 women together can complete the same work in 15 days. In how many days will 11 women complete the same work?
Option 1: 12
Option 2: 8
Option 3: 6
Option 4: 16
Correct Answer: 12
Solution :
Given, 5 men and 8 women can complete a work in 12 days working together
3 men and 7 women together can complete the same work in 15 days
Let the work done by a man and a woman in a day be $a$ and $b$ units
According to the question,
$5(12)a+8(12)b=3(15)a+7(15)b$
⇒ $15a = 9b$
⇒ $a=\frac{3}{5}b$
Also, $5(12)a+8(12)b=1$
⇒ $5\times 12\times \frac{3}{5}b+96b=1$
⇒ $132b=1$
or, $b=\frac{1}{132}$
Work done by 11 women in a day
= $11\times \frac{1}{132}$
= $\frac{1}{12}$
So, the time taken by 11 women to complete the work = 12 days
Hence, the correct answer is 12 days.
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