Postal or Sorting Assistants Model Paper 8 With Solutions

(b) Let A,B and C individualy complete the work in x,y andz days respectively.
$\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{1}{30}----\left(1\right)$
$\frac{1}{\mathit{y}}+\frac{1}{\mathit{z}}=\frac{1}{24}---\left(2\right)$
$\frac{1}{\mathit{z}}+\frac{1}{\mathit{x}}=\frac{1}{20}---\left(3\right)$
adding equ (1), (2) and (3)
$2\left[\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}+\frac{1}{\mathit{z}}\right]=\frac{1}{8}\Rightarrow \frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}+\frac{1}{\mathit{z}}=\frac{1}{16}---\left(14\right)$
A,B and C together complete the work in 16 days.
In 10 days they completed $\frac{10}{16}=\frac{5}{8}$ Part
Remaining work $=1-\frac{5}{8}=\frac{3}{8}$
Subtracting equ (2) from (4)
we get, $\frac{1}{\mathit{x}}=\frac{1}{48}\mathit{o}\mathit{r}\mathit{x}=48$
A alone can finish the Remaining work in
$\frac{3}{8}\times 48=18$days