Question : Two men and 7 women can complete a work in 28 days, whereas 6 men and 16 women can do the same work in 11 days. In how many days will 5 men and 4 women, working together, complete the same work?
Option 1: 20
Option 2: 18
Option 3: 14
Option 4: 22
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Correct Answer: 22
Solution : Given, 2 men and 7 women can complete a work in 28 days 6 men and 16 women can do the same work in 11 days Use the following formula to solve the question: $\frac{M_{1}\times D_{1}}{W_{1}}=\frac{M_{2}\times D_{2}}{W_{2}}$ Where $M_1$ and $M_2$ are men, $D_1$ and $D_2$ are days and $W_1$ and $W_2$ are work done. Let the efficiency of 1 man be M. And the efficiency of 1 woman is W. According to the question, 2 men and 7 women complete a work in 28 days = 6 men and 16 women complete the same work in 11 days ⇒ (2M + 7W) × 28 = (6M + 16W) × 11 ⇒ 56M + 196W = 66M + 176W ⇒ 10M = 20W ⇒ M = 2W 2 men and 7 women = 2M + 7W ⇒ 2 men and 7 women = 4W + 7W ⇒ 2 men and 7 women = 11W 5 men and 4 women = 5M + 4W ⇒ 5 men and 4 women = 10W + 4W ⇒ 5 men and 4 women = 14W $\frac{M_1D_1}{W_1}=\frac{M_2D_2}{W_2}$ ⇒ 11W × 28 = 14W × D2 ⇒ D2 = 22 days Hence, the correct answer is 22.
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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
Question : 4 men and 5 women can complete a work in 15 days, whereas 9 men and 6 women can complete it in 10 days. To complete the same work in 7 days, how many women should assist 4 men?
Option 1: 13
Option 2: 14
Option 3: 15
Option 4: 11
Question : 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 25 women complete it?
Option 2: 16
Option 3: 25
Option 4: 18
Question : 1 man and 4 women can complete a work in $\frac{65}{4}$ days, while 3 men and 4 women can complete it in $\frac{13}{2}$ days. In how many days will 13 women complete the same?
Question : 12 men and 12 women can complete a piece of work in 9 days. 6 men and 15 women can complete the same work in 12 days. How long (in days) would it take 9 women to complete half the work?
Option 1: 36
Option 2: 12
Option 3: 18
Option 4: 24
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