16 women take 12 days to complete a work which can be completed by 12 men in 8 days. 16 men started working and after 3 days 10 men left and 4 women joined them. How many days will they take to complete the remaining work? (Work & Time)

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

16 women can do the work in =12 days

$∴$ 1 women can do the work in = (16 $\times$ 12) days

$∴$ 1 women can in 1 days = $\frac{1}{12 \times 16}$ part of the work

Again, 12 men can do the work in = 8 days

$∴$ 1 man can do the work in = (8 $\times$ 12) days

$∴$ I man can in 1 days = $\frac{1}{8 \times 12}$ part of the work

$∴$ 16 men's 3 day's work = $\frac{1}{8 \times 12} \times 3 \times 16 = \frac{1}{2}$ part of the work

Remaining work = $1 - \frac{1}{2} = \frac{1}{2}$

Now, number of men still working = 16-10=6

$∴$ 6 men's 1 days work = $\frac{1}{12 \times 8} \times 6 = \frac{1}{16}$ part

And 4 men's 1 days work = $\frac{1}{12 \times 16} \times 4 = \frac{1}{48}$ part

$∴$ They can do in 1 day = $\frac{1}{16} + \frac{1}{48} = \frac{3 + 1}{48} = \frac{4}{48} = \frac{1}{12}$ part

Now, $\frac{1}{12}$ part of the work is done in = 1 day

$∴$ $\frac{1}{2}$ part of the work is done in = $\frac{12}{2}$ = 6 days.

1 year ago

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