Question

$A,B$ and $C$ can complete a work separately in $24,36$ and $48$ days respectively. They started together but $C$ left after $4$ days of start and $A$ left $3$ days before the completion of the work. In how many days will the work be completed ?

• A. $15$ days
• B. $22$ days
• C. $25$ days
• D. $35$ days

Answer 1

The correct option is A $15$ days

Let the total work be W

⇒Speed of A $=\frac{W}{24}$

⇒Speed of B $=\frac{W}{36}$

⇒Speed of C $=\frac{W}{48}$

Let the work takes x days .

Then

$\frac{W}{48}\times 4+\frac{W}{24}\times (x-3)+\frac{W}{36}\times x=W$

⇒ Solving we get $x=15$ days