SSC CPO SI and ASI 2012 Paper

(2)Let (A + C) complete the work in ‘a’ days. So B will complete the work in 3a days.
$\mathrm{}\frac{1}{\mathit{a}}+\frac{1}{3\mathit{a}}=\mathrm{}\frac{1}{10}\Rightarrow 3\mathit{a}=40\Rightarrow \mathit{a}=\frac{40}{3}$
Let (A + B) complete the work in ndays. So C will complete the work in2n days.
$\frac{1}{\mathit{n}}+\frac{1}{2\mathit{n}}=\frac{1}{10}\Rightarrow \mathit{n}=\mathrm{}\frac{30}{2}=15$
${\left(\mathit{A}+\mathit{B}+\mathit{C}\right)}^{\prime }\mathit{s}1$ day's work $=\mathrm{}\frac{1}{10}$$\mathrm{}\frac{1}{\mathit{A}}+\mathrm{}\frac{1}{40}+\frac{1}{30}=\mathrm{}\frac{1}{10}$
$\Rightarrow \frac{1}{\mathit{A}}=\mathrm{}\frac{12-3-4}{120}=\frac{5}{120}=\frac{1}{24}$
Therefore, A will complete the workin 24 days.