Question 61

A, B and C can independently finish a piece of work in 18 days, ‘x’ days and 27 days respectively. A and C started working together and after 6 days B replaced both of them. If B could finish the remaining work in 16 days, what is the value of ‘x’ ?

Solution

(A + C)'s 1 day's work = $$\frac{1}{18} + \frac{1}{27}$$

= $$\frac{3 + 2}{54} = \frac{5}{54}$$

=> (A + C)'s 6 day's work = $$\frac{5}{54} \times 6$$

= $$\frac{5}{9}$$

=> Remaining work = $$1 - \frac{5}{9} = \frac{4}{9}$$

Acc to ques,

=> $$\frac{16}{x} = \frac{4}{9}$$

=> $$x = \frac{16 \times 9}{4}$$

=> $$x = 4 \times 9 = 36$$ days

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