Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is

The correct answer is 340.

To solve this problem, we first need to determine the efficiency, which is the rate of work per day, for Ankita, Bipin, and Chandan.

Let the amount of work Chandan can do in one day (his efficiency) be defined as $1$ unit per day.

Since Bipin is twice as efficient as Chandan, Bipin's daily efficiency is:

$2\times 1=2$ units per day.

We are also told that Ankita is twice as efficient as Bipin. Therefore, Ankita's daily efficiency is:

$2\times 2=4$ units per day.

Next, we determine how many days each person contributed to the project. The problem states that all three individuals start working together, Bipin leaves after 20 days, and the entire job takes exactly 60 days to complete. This means:

Ankita worked for the full $60$ days.

Chandan worked for the full $60$ days.

Bipin worked for only $20$ days.

Now, we can calculate the total amount of work required for the entire job by summing up the work completed by each individual. The work done by a person is calculated as the product of their efficiency and the number of days they worked.

Ankita's total work contribution:

$4\times 60=240$ units of work.

Bipin's total work contribution:

$2\times 20=40$ units of work.

Chandan's total work contribution:

$1\times 60=60$ units of work.

The total work required for the entire job is the sum of these three amounts:

$240+40+60=340$ units of total work.

Finally, to find out how many days Chandan would need to complete this entire job by himself, we divide the total work by Chandan's daily efficiency rate (which is $1$ unit per day):

$\frac{340}{1}=340$ days.

Therefore, Chandan would take 340 days to complete the job alone.