Question

2 men and 3 boys can do a piece of work in 10- days while 3 men and 2 boys can finish it in 8 days. number of days taken by 2 men and 1 boy to finsh it will be

Answer 1

$\textbf {Hey there, here is the solution.}$

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STEP 1: Form the equations:

2 men and 3 boys can do a piece of work in 10 days

⇒ 2M + 3B = 10D

.

3 men and 2 boys can finish it in 8 days:

⇒3M + 2B = 8D

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STEP 2: Find 1 man in term of boys:

Since the work is the same:

(2 x 10)
M + (3 x 10)B = (3 x 8)M + (2 x 8)B

.

20M + 30B = 24M + 16B

24M - 20M = 30B - 16B

4M = 14B

1M = 3.5B

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STEP 3: Find 2 men and 1 boy in term of boys:

2M + 1B = 2(3.5B) + 1B = 8B

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STEP 4: Find the number of days needed if there is only 1 boy:

2M + 3B = 10D

2(3.5B) + 3B = 10D

10B = 10D

1B = 10 x 10

1B = 100 days

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STEP 4: Find the number of days needed if there were 8 boys:

1B = 100 days

8B = 100 ÷ 8 = 12.5 days

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Answer: 2 men and 1 boy need 12.5 days to finish the work.

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⭐$\textbf {Cheers}$⭐