Question : 22 boys, working together, can complete a work in 10 days, whereas 25 boys and 12 girls take 8 days to complete the same work. In how many days can only 6 girls, working together, complete the same work?
Option 1: 170
Option 2: 177
Option 3: 175
Option 4: 176
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Correct Answer: 176
Solution : Number of days taken by 22 boys to complete a work = 10 days Number of days taken by 25 boys and 12 girls to complete the same work = 8 days Let the efficiency of a boy = B The efficiency of a girl = G Total work = 22 × 10 × B = (25 × B + 12 × G) × 8 ⇒ 20 × B = 96 × G ⇒ $\frac{\text{B}}{\text{G}} = \frac{24}{5}$ Let B = 24k and G = 5k So total work = 22 × 10 × 24k The efficiency of a girl = 5k So, the required days = $\frac{22 × 10 × 24\text{k}}{5\text{k} × 6}$ = 22 × 8 = 176 days Hence, the correct answer is 176 days.
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Question : A and B together complete a work in 20 days, B and C together complete the same work in 30 days, and C and A together complete the same work in 24 days. In how many days A, B, and C together can complete the same work?
Option 1: 8 days
Option 2: 16 days
Option 3: 12 days
Option 4: 15 days
Question : 42 boys can complete a piece of work in 20 days working 8 hours per day. In how many days can 14 boys complete the same work, each boy working 12 hours per day?
Option 1: 39 days
Option 2: 40 days
Option 3: 41 days
Option 4: 42 days
Question : 12 men can complete a work in 6 days working 4 hours per day. If 4 men work 8 hours per day, then in how many days the same work will be completed?
Option 2: 6 days
Option 3: 9 days
Option 4: 10 days
Question : A, B, and C together can complete a work in 5 days. A and B together can complete the same work in 6 days. C alone can finish the same work in how many days?
Option 1: 60 days
Option 2: 30 days
Option 3: 15 days
Option 4: 20 days
Question : A, B, and C together can do a piece of work in 6 days. A and B together can do the same work in 12 days. B alone can do the same work in 18 days. In how many days can A and C together do the same work?
Option 1: 9 days
Option 2: 10.5 days
Option 3: 8 days
Option 4: 7.5 days
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