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's denote the total work as $W$.

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

Let $A$, $B$, and $C$ be the individual efficiencies of Amal, Vimal, and Sunil, respectively. From the given information, we can form the following equations:

1. $A + B = \frac{W}{150}$ 

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

Now, let's analyze the second scenario where they work on alternate days: Amal works on all days, so his work in one day is $A$. Vimal works on every second day, so his work in two days is $B$. Sunil works on every third day, so his work in three days is $C$.

So, in 6 days, they complete $A + B + C$ work.

To find the total number of days required, we need to find how many times 6 divides the total work $W$. We can calculate this by dividing $W$ by the work done in 6 days:

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

We can solve the equations for $A$, $B$, and $C$ and substitute them into the above equation to find the total number of days.

After solving, we get the total number of days as 139.