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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