Question

Tick (✓) the correct answer:
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

Answer 1

(d) 48 days

$$\begin{gathered} \mathrm{A}\mathrm{can}\mathrm{do}\mathrm{a}\mathrm{job}\mathrm{in}16\mathrm{days}. \\ \mathrm{B}\mathrm{can}\mathrm{do}\text{the}\mathrm{job}\mathrm{in}12\mathrm{days}. \\ \text{Suppose}\mathrm{C}\mathrm{can}\mathrm{do}\text{the}\mathrm{job}\mathrm{in}\mathrm{x}\mathrm{days}. \\ \mathrm{A}\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{16} \\ \mathrm{B}\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{12} \\ \mathrm{C}\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{\mathrm{x}} \\ \mathrm{A},\mathrm{B}\mathrm{and}\mathrm{C}\mathrm{together}\mathrm{can}\mathrm{complete}\mathrm{the}\mathrm{work}\mathrm{in}6\mathrm{days}. \\ (\mathrm{A}+\mathrm{B}+\mathrm{C})\text{'}\mathrm{s}1\mathrm{day}\mathrm{work}=\frac{1}{6} \\ \mathrm{Therefore},\frac{1}{6}=\frac{1}{16}+\frac{1}{12}+\frac{1}{\mathrm{x}} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{1}{6}-\frac{1}{16}-\frac{1}{12}=\frac{8-3-4}{48}=\frac{1}{48} \\ \mathrm{x}=48 \\ \mathrm{Therefore},\mathrm{C}\mathrm{alone}\mathrm{can}\mathrm{complete}\mathrm{the}\text{job}\mathrm{in}48\mathrm{days}. \end{gathered}$$