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A piece of work is completed by 3 men and 4 boys in 7 days. The same piece of work is completed by 5 men and 3 boys in 6 days. Find the time taken by 1 man and 2 boys to complete the 4 times of the same work?1. 55 days2. 66 days3. 59 days4. 69 days5. 60 days |
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Answer» Correct Answer - Option 2 : 66 days Given: A piece of work is completed by 3 men and 4 boys in 7 days. The same piece of work is completed by 5 men and 3 boys in 6 days Formula used: Work = Time × Efficiency Calculation: Let the efficiency of a man be M And the efficiency of a boys be B Now, using the first given condition ⇒ Total work = (3M + 4B) × 7 ⇒ Total work = 21M + 28B ----(1) Use the second given condition ⇒ Total work = (5M + 3W) × 6 ⇒ Total work = 30M + 18W ----(2) By equating equation (1) and (2) we get ⇒ 21M + 28B = 30M + 18W ⇒ 30M - 21M = 28B - 18W ⇒ 9M = 10B ⇒ M/B = 10/9 So, the ratio of efficiency of man and boy is 10 : 9 ⇒ Time work = 21 × 10 + 28 × 9 ⇒ Time work = 462 Four times of the total work is ⇒ 462 × 4 = 1848 The total efficiency of 1 man and 2 boys ⇒ 1 × 10 + 2 × 9 ⇒ 10 + 18 = 28 ⇒ Time = 1848/28 = 66 days ∴ 1 man and 2 boys will complete the four times of the same work in 66 days. |
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