Question : 8 men and 12 women finish a job in 4 days. While 6 men and 14 women in 5 days. In how many days will 20 women finish the job?
Option 1: 10
Option 2: 20
Option 3: 30
Option 4: 15
Correct Answer: 20
Solution :
Let the work rate of one man is M and the work rate of one woman is W.
According to the question,
8M + 12W = $\frac{1}{4}$ ------------------(1)
6M + 14W = $\frac{1}{5}$ ------------------(2)
Solving this system of equations,
⇒ M = $\frac{1}{8}$($\frac{1}{4}$ – 12W)
⇒ M = $\frac{1}{32}$ – $\frac{3}{2}$W ---------------(3)
From equation (2),
⇒ 6[$\frac{1}{32}$ – $\frac{3}{2}$W] + 14W = $\frac{1}{5}$
⇒ $\frac{3}{16}$ + 5W = $\frac{1}{5}$
⇒ 5W = $\frac{1}{80}$
⇒ W = $\frac{1}{400}$
This means that one woman can finish the job in 400 days.
Now, the time is taken for 20 women to finish the job = $\frac{400}{20}$ = 20 days
Hence, the correct answer is 20.
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