Question

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days find the time taken by one boy alone to finish the work

Answer 1

8 men and 12 boys finished the work in 10 days

8M + 12B = 10D

6 men and 8 boys finished the work in 14 days

6M + 8B = 14D

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Since both statements are referring to the same work:

(8 x 10)M + (12 x 10)B = (6 x 14)M + (8 x 14)B

80M + 120B = 84M + 112B

84M - 80M = 120B - 112B

4M = 8B

1M = 2B

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Substitute 1M = 2B into 8M + 12B = 10D:

8(2B) + 12B = 10D

16B + 12B = 10D

28B = 10D

.

28 Boys take 10 days to finish the work.

⇒ 1 Boy will need (28 x 10 = 280) days to finish the work.

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Answer: 1 boy will take 280 days to finish the work.