Question:

A can do a job in 16 days and B can do the same job in 12 days. With the help of C, they can finish the job in 6 days only. Then, C alone can finish it in

(a) 34 days

(b) 22 days

(c) 36 dyas

(d) 48 days

Solution:

(d) 48 days

A can do a job in 16 days.

B can do the job in 12 days.

Suppose $\mathrm{C}$ can do the job in $\mathrm{x}$ days.

A’s 1 day work $=\frac{1}{16}$ B’s 1 day work $=\frac{1}{12}$ C’s 1 day work $=\frac{1}{x}$

$\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ together can complete the work in 6 days.

$(\mathrm{A}+\mathrm{B}+\mathrm{C})$ ‘s 1 day work $=\frac{1}{6}$

Therefore, $\frac{1}{6}=\frac{1}{16}+\frac{1}{12}+\frac{1}{\mathrm{x}}$

$\Rightarrow \frac{1}{\mathrm{x}}=\frac{1}{6}-\frac{1}{16}-\frac{1}{12}=\frac{8-3-4}{48}=\frac{1}{48}$

$\mathrm{x}=48$

Therefore, $\mathrm{C}$ alone can complete the job in 48 days.