A and B can complete a certain work in 24 days and 42 days respectively. A started the work and after x days, B joined him and the whole work was completed in 20 days. The value of x is:

A and B can complete a certain work in 24 days and 42 days respectively.

LCM of 24 and 42 is 168 which can be assumed as the total work.

The efficiency of A = $$\frac{168}{24}$$ = 7 units/day

The efficiency of B = $$\frac{168}{42}$$ = 4 units/day

A started the work and after x days, B joined him and the whole work was completed in 20 days.

$$7\times20 + 4\times(20-x) = 168$$

$$7\times5 + (20-x) = 42$$

35 + (20-x) = 42

(20-x) = 42-35

(20-x) = 7

x = 20-7 = 13