A can do a piece of work in 45 days and B in x days. A starts the work and works for 15 days, then B joins and together they work for 12 more days to complete the work. Find the value of x.

30

A's work of 1 day = \(\frac{1}{45}\)

Work done in 15 days = \(\frac{15}{45}\) = \(\frac{1}{3}\)

Therefore, one - third of the work is done 

Remaining work is done by A and B together in 12 days 

A and B will complete the total work in 18 days

Efficiency of B = 5 - 2 = 3

Time taken by B alone to complete the work = \(\frac{Total\; work}{Efficiency}\)

                                                                = \(\frac{90}{3}\) = 30 days