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.

Step 1: Define the efficiencies of Ankita, Bipin, and Chandan.

Let Chandan's efficiency (work done per day) be $x$ units/day.

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

$\text{Bipin's efficiency}=2x$

Since Ankita is twice as efficient as Bipin, Ankita's efficiency is:

$\text{Ankita's efficiency}=2\times 2x=4x$

Step 2: Calculate the total work done.

All three work together for the first 20 days.

Combined efficiency of Ankita, Bipin, and Chandan per day:

$\text{Combined efficiency (all three)}=4x+2x+x=7x$

Work completed in the first 20 days by all three:

$\text{Work done in first 20 days}=20\times 7x=140x$

After 20 days, Bipin leaves. Ankita and Chandan work together for the remaining duration.

Since the total job got completed in 60 days, the remaining time worked by Ankita and Chandan is:

$\text{Remaining days}=60-20=40\text{days}$

Combined efficiency of Ankita and Chandan per day:

$\text{Combined efficiency (Ankita + Chandan)}=4x+x=5x$

Work completed in the remaining 40 days by Ankita and Chandan:

$\text{Work done in remaining 40 days}=40\times 5x=200x$

Total work done to complete the job:

$\text{Total Work}=140x+200x=340x$

Step 3: Calculate the number of days Chandan needs to complete the job alone.

Chandan's efficiency is $x$ units/day.

Time required for Chandan alone to finish the total work of $340x$:

$\text{Number of days}=\frac{340x}{x}=340\text{days}$

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