Question

$A$ and $B$ can do a work in $10$ days. $B$ and $C$ can do the same work in $15$ days. $C$ and $A$ can complete the same work in $20$ days. In how many days can $C$ alone complete the work ?

• A. $120$ days
• B. $118$ days
• C. $115$ days
• D. $110$ days

Answer 1

The correct option is A $120$ days

In 10 days $A$ and $B$ does 1 work.

$\therefore$ In 1 day $A$ and $B$ will do $\frac{1}{10}$ work -(i)

In 15 days $B$ and $C$ does 1 work

$\therefore$ In 1 day $B$ and $C$ will do $\frac{1}{15}$ work -(ii)

In 20 days $C$ and $A$ does 1 work

$\therefore$ In 1 day $C$ and $A$ will do $\frac{1}{20}$ work - (iii)

Adding equation(i),(ii)and (iii)

$In1$ day $2(A+B+C)$ will $do(\frac{1}{10}+\frac{1}{15}+\frac{1}{20})$

$In1$ day $2(A+B+C)$ will $do$ $\frac{13}{60}$

work.

In 1 day $(A+B+C)$ will $do\frac{13}{120}$ work

In 1 d a y$(A+B)+\left(C\right)$ will $do\frac{13}{120}$ work

$A+B$ does $\frac{1}{10}$ work in 1 day

$\therefore$ work done by C in 1 day

$=\frac{13}{120}-\frac{1}{10}$

$=\frac{1}{120}$

$\frac{1}{120}$ work is done by $C$ in 1 day.

$\therefore 1$ work is done by $C$ in 120 days.

Answer: option $\left(A\right)$