Question

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? (a) 20 (b) 30 (c) 26 (d) 28 (e) 24

Answer 1

1 man's work in one day= 1/(18*30)=1/540
1 woman's work in one day=1/(16*36)=1/576
work by 15 men in 9 days=15*9/540=1/4
remaining work= 1-1/4=3/4
18 women's work on one day= 18/576=1/32
time taken to complete the job= (3/4)*32=24 days

Answer 2

18 women will complete the remaining work in (e) 24 days.

Given: 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.

To Find: no. of days taken by 18 women to complete the remaining work.

Solution: Let work be done by 15 men in 9 days = $W_2$

$\frac{M_1D_1}{W_1} =\frac{M_2D_2}{W_2}$

$\frac{18(30)}{1}=\frac{15(9)}{W_2}$

⇒ $W_2$ = $\frac{15(9)}{18(30)}$ = $\frac{1}{4}$

Remaining work = $1-\frac{1}{4}$ = $\frac{3}{4}$

16 women can complete the same project in 36 days, $\frac{M_1D_1}{W_1}= \frac{M_2D_2}{W_2}$

⇒$\frac{16(36)}{1} = \frac{18(D_2)}{3/4}$

⇒18 × $D_2$ =  $\frac{3}{4}$ × 16 × 36

$D_2=$ 24 days.

So, 18 women will complete the remaining work in (e) 24 days.

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