4 boys or 7 girls can complete a piece of work in 18 days. How many days will 12 boys and 21 girls together take to complete this job?

4 boys or 7 girls can complete a piece of work in 18 days.

It means that 4 boys = 7 girls.    Eq.(i)

Let's assume the time taken by 12 boys and 21 girls together to complete this job is 'y'.

7 girls $$\times$$ 18 = (12 boys+21 girls) $$\times$$ y

7 girls $$\times$$ 18 = (3$$\times$$ 4 boys+21 girls) $$\times$$ y

Put Eq.(i) in the above equation.

7 girls $$\times$$ 18 = (3$$\times$$ 7 girls+21 girls) $$\times$$ y

126 girls = (21 girls+21 girls)y

126 girls = 42 girls $$\times$$ y

y = 3

So the time taken by 12 boys and 21 girls together to complete this job is 3 days.