The ratio of the work done by 50 women to the work done by 25 men, in the same time is 4 : 3. If 18 women and 12 men can finish a piece of work in 5 days, then how many women can finish the same work in 20/3 days?

Solution

Given:
– The ratio of the work done by 50 women to the work done by 25 men in the same time is 4:3.
– 18 women and 12 men can finish a piece of work in 5 days.

Step 1: Find the ratio of work done by one woman to one man

Let the work done by one woman in one day be \(W\) and the work done by one man in one day be \(M\).
\[ \frac{50W}{25M} = \frac{4}{3} \]
\[ \frac{W}{M} = \frac{4}{3} \times \frac{1}{2} = \frac{2}{3} \]

Step 2: Calculate the total work done

Total work done by 18 women and 12 men in 5 days:
\[ \text{Total work} = (18W + 12M) \times 5 \]
Using the ratio \(W = \frac{2}{3}M\):
\[ \text{Total work} = \left(18 \times \frac{2}{3}M + 12M\right) \times 5 = (12M + 12M) \times 5 = 24M \times 5 = 120M \]

Step 3: Calculate how many women can finish the work in \(20/3\) days

Let the number of women required be \(x\). They need to do the total work in \(20/3\) days:
\[ xW \times \frac{20}{3} = 120M \]
Using the ratio \(W = \frac{2}{3}M\):
\[ x \times \frac{2}{3}M \times \frac{20}{3} = 120M \]
\[ x = \frac{120 \times 3}{\frac{2}{3} \times 20} = \frac{360}{\frac{40}{3}} = \frac{360 \times 3}{40} = 27 \]

Conclusion

27 women can finish the same work in \(20/3\) days.