A,B and C together can complete a task in 16 days. After, three of them worked together for 2 days, A left. B and C continued for 9 more days, and then B left. C completed the remaining work in 6 days. If C alone can complete the entire task in 24 days, then in how many days B alone can complete it?

Correct option is A

Given:

A, B and C together can complete a task in 16 days.

After 2 days, A left. B and C continued for 9 more days and then B left.

C completed the remaining work in 6 days.

C alone can complete the task in 24 days.

Formula used:

Work rate of A, B, and C together = $$\frac{1}{16}$$​ work/day

Work rate of C = $$\frac{1}{24}$$​ work/day

Solution:

Let work rate of A be A, B be B, and C be C.

A + B + C = $$\frac{1}{16}$$​​

C = $$\frac{1}{24}$$​​

Work done by A, B, and C in 2 days:

2 × (A + B + C) = $$\frac{2}{16}=\frac{1}{8}$$​​

Work done by B and C in 9 days:

9 × (B + C) = 9 × (B + $$\frac{1}{24}$$​)

Work done by C in 6 days:

6 × $$\frac{1}{24}=\frac{1}{4}$$​​

Total work done by A, B, and C:

$$\frac{1}{8}$$​ + 9(B + $$\frac{1}{24}$$​) + $$\frac{1}{4}$$ = 1

=>$$\frac{1}{8}+9B+\frac{9}{24}+\frac{1}{4}=1$$

=>$$\frac{1}{8}+9B+\frac{3}{8}+\frac{1}{4}=1$$​​​

=> $$\frac{4}{8}+9B+\frac{2}{8}=1$$​

=> $$\frac{6}{8}$$​ + 9B = 1

​$$=> \frac{3}{4} + 9B = 1=> 9B = 1 - \frac{3}{4}=> 9B = \frac{1}{4}=> B = \frac{1}{36}$$​​

∴ B alone can complete the task in 36 days.