RRB Paramedical Staff Nurse Model Paper 3

Given, Time taken by $\left(\mathit{A}+\mathit{B}\right)$ to fill the tank $=6\mathit{h}$
Thus, part of tank filled by A + B in $1\mathit{h}=\frac{1}{6}$ ..... (i)
(if a pipe fills a tank in $\mathit{x}$ h, then the part of tank filled in $1\mathit{h}=\frac{1}{\mathit{x}}$)
Similarly, part of tank filled by (B + C) in $1\mathit{h}$. $=\frac{1}{10}$.....(ii)
And part of tank filled by (C + A) in $1\mathit{h}=\frac{2}{15}$......(iii)
Now, part of tank filled by (A + B + C) in $1\mathit{h}$
On adding Esq. (i), (ii), (in), we get
$\mathrm{A}+\mathrm{B}+\mathrm{B}+\mathrm{C}+\mathrm{C}+\mathrm{A}$
$=\frac{1}{6}+\frac{1}{10}+\frac{2}{15}$
$\Rightarrow 2\mathit{A}+2\mathit{B}+2\mathit{C}=\frac{5+3+4}{30}$
$\Rightarrow 2\left(\mathit{A}+\mathit{B}+\mathit{C}\right)=\frac{12}{30}$
$\Rightarrow \left(\mathit{A}+\mathit{B}+\mathit{C}\right)=\frac{12}{60}$
$\Rightarrow \left(\mathit{A}+\mathit{B}+\mathit{C}\right)=\frac{1}{5}$
Hence, A, B and C all three can fill the tank in 5h
(if a pipe fills $\frac{1}{\mathit{x}}$ part of the tank in $1\mathit{h}$, then the time taken by the pipe to fill the full tank $=\mathit{x}\mathit{h}$ )