Question

$A$ is $50\%$ as efficient as $B$. $C$ does half of the work done by $A$ and $B$ together. If $C$ alone does the work in $40$ days, then $A,B$ and $C$ together can do the work in

• A. $15\frac{1}{3}$ days
• B. $15$ days
• C. $13$ days
• D. $13\frac{1}{3}$ days

Answer 1

The correct option is D $13\frac{1}{3}$ days

$WorkRate=\frac{Work}{Days}$

Let Work Rate of A be $W_A$ and Work rate of B be $W_B$

and it is Given That

$\Rightarrow W_A=\frac{W_B}{2}$

$\Rightarrow \frac{W}{D_A}=\frac{W}{2D_B}$

$\Rightarrow D_B=\frac{D_A}{2}$...............................................(1)

Now, Work Done By$A$ and$B$ Together

$\Rightarrow \frac{W}{D_A}+\frac{W}{D_B}=\frac{3W}{2D_B}$

Using Given Information,

$\Rightarrow \frac{W}{D_C}=\frac{3W}{4D_B}$

$\Rightarrow \frac{W}{40}=\frac{3W}{4D_B}$

$\Rightarrow D_B=30$

From Relation (1) $\Rightarrow D_A=60$

Now,When $A,B$ and $C$ work Together

$\Rightarrow \frac{W}{30}+\frac{W}{60}+\frac{W}{40}=\frac{W}{\frac{120}{9}}$

Therefore The Work will be completed in $\frac{120}{9}days=13\frac{1}{3}days$

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