Question : 8 men or 10 boys can complete a work in 174 days. 12 men and 14 boys will complete the same work in how many days?
Option 1: 60 days
Option 2: 50 days
Option 3: 72 days
Option 4: 84 days
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Correct Answer: 60 days
Solution : Let M is the work done by one man in one day, B is the work done by one boy in one day and D is the number of days. According to the problem, 8 men or 10 boys can complete the work in 174 days. This means that the work done by 8 men in one day is equal to the work done by 10 boys in one day. ⇒ 8M = 10B ⇒ B = $\frac{4}{5}$M The total work done as the work done by one man in one day times the number of days it takes for 8 men to complete the work: ⇒ Total work (W) = 8M × 174 The required days it would take for 12 men and 14 boys to complete the same work is D. ⇒ W = (12M + 14B) × D Since both expressions are equal to W, ⇒ 8M × 174 = (12M + 14B) × D Substituting B = $\frac{4}{5}$M from the first equation into the second equation gives, ⇒ 8M × 174 = (12M + 14 × $\frac{4}{5}$M) × D ⇒ D = $\frac{1392\times5}{116}$ = 60 Hence, the correct answer is 60 days.
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Question : 12 men can do work in 8 days while 4 boys can do it in 40 days. In how many days 9 boys and 3 men together will complete the same work?
Option 1: 10 days
Option 2: $\frac{280}{13}$ days
Option 3: $\frac{80}{7}$ days
Option 4: $\frac{260}{17}$ days
Question : 4 men and 8 women complete a job in 10 days and 5 men and 24 women complete the same work in 4 days. In how many days will 1 man and 1 woman complete the same work?
Option 1: $63 \frac{1}{3}$ days
Option 2: $69 \frac{7}{9}$ days
Option 3: $67 \frac{1}{3}$ days
Option 4: $62 \frac{2}{9}$ days
Question : 16 women take 12 days to complete a work which can be completed by 12 men in 8 days. 16 men started working and after 3 days 10 men left and 4 women joined them. How many days will it take them to complete the remaining work?
Option 1: 4
Option 2: 6
Option 3: 8
Option 4: 10
Question : 40 men can complete a work in 18 days. Eight days after they started working together, 10 more men joined them. How many days will it now take to complete the remaining work?
Option 1: 6
Option 2: 8
Option 3: 10
Option 4: 12
Question : 3 men or 5 women can do a work in 57 days. In how many days can 9 men and 4 women do that same work?
Option 1: 16 days
Option 2: 18 days
Option 3: 14 days
Option 4: 15 days
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