A can do \(\frac{2}{5}\)th work in 48 days and B can do \(\frac{3}{5}\)th of same work in 96 days. If A and B start working together and worked for X days and after that C also joined them and remaining work is completed in next (X-15) days. If efficiency of C is \(\frac{1}{3}\)rd of B. Find in (X+20) days how much percent of work is done by A and C?

62.5%

⇒ A does \(\frac{2}{5}\) of the work in = 48 days

So, A finish the whole work alone in = \(\frac{5}{2}\) × 48 = 120

⇒ B does \(\frac{3}{5}\) of the work in = 96 days

So, B finish the whole work alone in = \(\frac{5}{3}\) × 96 = 160

Now, 

                  A   :        B      :       C

Efficiency :  4   :       3       :       1      [C's Effi. = \(\frac{1}{3}\) of B]

ATQ,

⇒ (A + B) (x) + (A + B + C) (x-15) = Total work

⇒ (4 + 3) x + (4 + 3 + 1) (x-15) = 480

⇒ 7x + 8x - 120 = 480

⇒ 15 x = 600

⇒ x = 40

Therefore,

Work done by (A + C) in (X + 20) days = (x + 20) × (4 + 1)

                                                             = 60 × 5 = 300

Req. Percentage = \(\frac{300}{480}\) × 100 = 62.5%