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:

13

A = 24 days, B = 42 days,

⇒ A worked for x days alone = 7x

⇒ Then B joined him and whole work was completed in 20 days, therefore,

⇒ \(\frac{168 - 7x}{11}\) = 20 - x

⇒ 168 - 7x = 220 - 11x

⇒ 11x - 7x = 220 - 168

⇒ 4x = 52

⇒ x = 13.