Question

A can do a piece of work in $5$ days and B can do the same work in $20$ days. In the same assignment, they work together for $2$ days. Due to some emergency, they opted out from this assignment after working together for $2$ days. Then to complete the pending work, C joined who is half as efficient as A. How many days C will take to finish the remaining work ?

• A. $5$
• B. $7$
• C. $4$
• D. $10$

Answer 1

The correct option is A $5$

$\to$ In one day A can do ${\left(\frac{1}{5}\right)}^{th}$ of the total work and B can do ${\left(\frac{1}{20}\right)}^{th}$ of the total work.

$\to$ Thus in one day A and B together can complete $(\frac{1}{20}+\frac{1}{5})$ of the total work i.e., ${\left(\frac{1}{4}\right)}^{th}$ of work.

$\to$ It is given that A and B together worked for $2$ days.

$\therefore 2\times \frac{1}{4}=\frac{1}{2}$
$\to$ In two day A & B together finished half of work.

$\to$ C is half as efficient A, thus C can finish the given work in twice the no. of days in which A finishes it. Thus, C will take $10$ days to finish it.

$\to$ In one day C will complete ${\left(\frac{1}{10}\right)}^{th}$ of total work

$\to$ Let $x$ be the no. of days that C takes to finish remaining half work.

$x=\frac{1}{10}=\frac{1}{2}$ $\Rightarrow$ $\therefore n=5$