A can do 50% of the job in 16 days. B can do one-fourth of the same job in 24 days. Working together, in how many days they can do seven-fourth of the job?

A can do 50% of the job in 16 days.

A can complete the whole work alone in $$16\times2$$ = 32 days.

B can do one-fourth of the same job in 24 days.

B can complete the whole work alone in $$24\times4$$ = 96 days.

The LCM of 32 and 96 is 96 which can be assumed as the total work.

Efficiency of A = $$\frac{96}{32}$$ = 3 units/day

Efficiency of B = $$\frac{96}{96}$$ = 1 unit/day

Number of day taken by both of them working together to do seven-fourth of the work = $$\frac{96\times\ \frac{7}{4}}{\left(3+1\right)}$$

= $$\frac{24\times\ 7}{4}$$

= $$6\times7$$

= 42 days