Question

If 6men or 8 women can reap a field in 86 days,how long will take 14 men and women take to reap it

Answer 1

Given:

6 men or 8 women can reap a field in 86 days

To find:

How long will take 14 men and women take to reap it?

Solution:

Let's assume,

"M" → represents the no. of 1 man

"W" → represents the no. of 1 woman

We have, 6 men or 8 women both take 86 days to reap the field

i.e., 6 M = 8 W

⇒ M = $\frac{8}{6} W$

⇒ M = $\frac{4}{3} W$

∴ $14M + 1W = [14\times \frac{4}{3}]W + 1W = \frac{56}{3}W + 1W= \frac{56+3}{3}W = \frac{59}{3}W$ ≈ $20W$

Now, we have the Man-Days formula as,

$\boxed{\bold{M_1 \times D_1 = M_2 \times D_2}}$

By substituting M₁ = 8W, D₁ = 86 & M₂ = 20W, we get

$8\times 86 = 20\times D_2$

$\implies 688 = 20 \times D_2$

$\implies D_2 = \frac{688}{20}$

$\implies \bold{D_2 = 34.4\:days}$

Thus, 14 men and woman will take 34.4 days to reap the field.

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