Question 45

18 men can complete a project in 30 days and 16 women can complete the same project in 36 days. 15 men start working and after 9 days they are replaced by 18 women. In how many days will 18 women complete the remaining work ?

Solution

$$\frac{M1D1}{W1}$$ = $$\frac{M2D2}{W2}$$

W1=W2 = Q

$$\frac{18Mx30}{Q}$$ = $$\frac{16Wx36}{Q}$$

M = $$\frac{32}{30}$$W ....(1)

Let the days required by 18 women to complete the remaining work = y days

so $$\frac{(15M\times9)+(18W \times y)}{Q}$$ = $$\frac{16W\times36}{Q}$$ ......(2)

using equation 1 and 2

$$\frac{(16W\times9)+(18W \times y)}{Q}$$ = $$\frac{16W\times36}{Q}$$

144W + 18Wy = 576W

18Wy = 432 W

y = 24 days

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