Question

Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

Answer 1

Correct Answer: 139

Let the total work be $W$.

Amal and Vimal together complete $W$ work in 150 days, meaning their combined efficiency is $\frac{W}{150}$. Vimal and Sunil together complete $W$ work in 100 days, meaning their combined efficiency is $\frac{W}{100}$.

Let $A$, $B$, and $C$ represent the individual daily work rates of Amal, Vimal, and Sunil, respectively. Based on the information given, we can write these equations:

1. $A + B = \frac{W}{150}$

2. $B + C = \frac{W}{100}$

Now, consider the scenario where they work on alternate days: Amal works every day, contributing $A$ to the work daily. Vimal works every second day, contributing $B$ over two days. Sunil works every third day, contributing $C$ over three days.

Therefore, in a 6-day cycle, their combined work is $A + B + C$.

To determine the total days needed, we need to find how many 6-day cycles are required to complete the total work $W$. This can be calculated by dividing the total work by the work completed in 6 days:

Total days = $\frac{W}{A + B + C}$

We can solve the system of equations for $A$, $B$, and $C$ and then substitute these values into the formula above to find the total number of days.

The calculation shows that the total number of days required is 139.