4 men and 5 women can earn ₹8,800 in 8 days. 7 men and 10 women can earn ₹10,250 in 5 days.In how many days will 8 men and 12 women earn ₹21,600?

4 men and 5 women can earn ₹8,800 in 8 days. 7 men and 10 women can earn ₹10,250 in 5 days.

$$\frac{8\left(4M+5W\right)}{8800}\ =\ \frac{5\left(7M+10W\right)}{10250}$$

$$\frac{\left(4M+5W\right)}{1100}\ =\frac{\left(7M+10W\right)}{2050}$$

$$\frac{\left(4M+5W\right)}{22}\ =\frac{\left(7M+10W\right)}{41}$$

$$164M+205W\ =154M+220W$$

$$164M\ -154M=220W\ -\ 205W$$

2M = 3W    Eq.(i)

Let's assume 8 men and 12 women can earn ₹21,600 in 'y' days.

$$\frac{8\left(4M+5W\right)}{8800}\ =\ \frac{y\left(8M+12W\right)}{21600}$$

Put Eq.(i) in the above equation.

$$\frac{8\left(6W+5W\right)}{8800}\ =\ \frac{y\left(12W+12W\right)}{21600}$$

$$\frac{8\times11W}{8800}\ =\ \frac{y\times\ 24W}{21600}$$

$$\frac{88}{8800}\ =\ \frac{y\times\ 24}{21600}$$

8 men and 12 women can earn ₹21,600 in 9 days.