12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required?

(Work & Time)

প্রশ্নে বলা হচ্ছে যে, 12 জন পুরুষ একটি কাজ করে 36 দিনে, 18 জন নারী কাজটি করে 60 দিনে। এখন ৪ জন পুরুষ ও 20 জন নারী একত্রে 20 দিন কাজটি করলো। বাকি কাজ  4 দিনে শুধু নারীদের দিয়ে করালে কতজন নারী লাগবে?

12 men take 36 days to complete = 1 work

∴ 1 men take 1 days to complete $= \frac{1}{12 \times 36}$ part of work

∴ 8 men take 20 days to complete $= \frac{8 \times 20}{12 \times 36} = \frac{10}{27}$ part of work

Again, 18 women take 60 days to complete = 1 work

∴ 1 women take 1 days to complete $= \frac{1}{18 \times 36}$ part of work

∴ 20 women take 20 days to complete $= \frac{20 \times 20}{18 \times 60} = \frac{10}{27}$ part of work

So, 8 men and 20 women have done in 20 days $= \left(\frac{10}{27} + \frac{10}{27}\right) = 2 \times \frac{10}{27} = \frac{20}{27}$ parts of work

∴ Remaining $= \left(1 - \frac{20}{27}\right) = \frac{27 - 20}{27} = \frac{7}{27}$ parts of work

Now, in 1 day $\frac{1}{18 \times 60}$ part of work is completed by = 1 women

∴ In 4 day  $\frac{7}{27}$ part of work is completed by $= \frac{18 \times 60 \times 7}{4 \times 27}$ = 70 women