Question

$A$ completes a work in $12$ days. $B$ completes the same work in $15$ days. $A$ started working alone and after $3$ days $B$ joined him. How many days will they now take together to complete the remaining work?

• A. $6$
• B. $8$
• C. $5$
• D. $4$
• E. None of these

Answer 1

Answer: (C)

$5$

Let us Find the Work Rate $(=\frac{W}{Days/Time})$

Now, Let us Assume $x$ be the Number of Extra Days.

$\left(i\right)$ for $A=\frac{W}{12}$

$\left(ii\right)$ for $B=\frac{W}{15}$

$\Rightarrow$ $\frac{W}{12}(3+x)+\frac{W}{15}x=W$

$\Rightarrow$$\frac{3+x}{12}+\frac{x}{15}=1$

$\Rightarrow$ $x=5$

Therefore Answer is $\left(C\right)$