A man can finish a work in 12 days while B can finish the same work in 15

Question

A man can finish a work in 12 days while B can finish the same work in 15 days. If both work together, then calculate the time taken to complete the work.

Options:

A . 6(23) days

B . 6 days

C . 8 days

D . 6(34) days

Answer: Option A
:
A
A can finish the work in 12 days.
He can finish

100 %

of the work in 12 days.
In 1 day he can finish

(\frac{100}{12}) % = 8.33 %

of the work.
Similarly B can finish

(\frac{100}{15}) % = 6.67 %

of the work in 1 day.
When they both work together, they can finish

(8.33 + 6.67) % = 15 %

of the work in 1 day
So, to complete

100 %

of the work, they will take

(\frac{100}{15}) e = 6 (\frac{2}{3})

days. Hence option (a).
2nd method:-Total work (W) = 12A = 15B ,

B = \frac{4}{5} A

n(A+B) = W = 12A or 15B (Here, we take 12A).

n (A + B) = 12 A, n (A + \frac{4}{5} A), n = \frac{20}{3} = 6 (\frac{2}{3})

days. Option (a).

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