Question

A can lay a railway track between two given stations in $16$ days and B can do the same job in $12$ days. With help of C, they did the job in $4$ days only. How many days will C take to do the job alone?

• A. 10 days
• B. 9 days
• C.
• D.

Answer 1

Answer: (D)

Given:

A can finish the work in $16$ days,

So, The part of the work done by A in one day $=\frac{1}{16}$

B can finish the work in $15$ days

So, The part of the work done by B in one day $=\frac{1}{12}$

A, B, C can finish the work in $4$ days

So, The part of the work done by A, B and C in one day $=\frac{1}{4}$

$\Rightarrow$ the part of the work done by C in one day $=\frac{1}{4}-(\frac{1}{16}+\frac{1}{12})$

$=\frac{1}{4}-\left(\frac{3+4}{48}\right)$

$=\frac{1}{4}-\frac{7}{48}$

$=\frac{12-7}{48}$

$=\frac{5}{48}$

i.e., C can finish the work in $\frac{48}{5}$ days $=9\frac{3}{5}$ days.

Hence, Option D is correct.