Priya and Rahul started a project together, and after 'k' days, Priya left and Rahul finished the remaining project in 8 days. The time taken by Rahul and Priya alone to complete the whole project are in the ratio 2:1 respectively. If Rahul can complete the entire project in 20 days, then calculate the value of 'k'.

Given:

Rahul's time to complete the project = 20 days

Ratio of Rahul : Priya = 2 : 1 → So Priya's time = 10 days

Rahul finishes remaining work in 8 days

Let k = number of days Priya worked with Rahul at the beginning

Work done is 1 (whole project)

Work rates:

Rahul’s 1 day work = 1/20

Priya’s 1 day work = 1/10

Together, in 1 day, they do:

(1/10 + 1/20) = (2 + 1)/20 = 3/20 of the work per day

Work done in first k days:

Work done together in k days =

k × 3/20 = 3k/20

Remaining work =

1 − 3k/20 = (20 − 3k)/20

Rahul finishes remaining work in 8 days:

Rahul’s 1-day work = 1/20

So in 8 days = 8/20 = 2/5

Now equate:

(20 − 3k)/20 = 2/5

Multiply both sides by 20:

20 − 3k = 8

⇒ 3k = 12

⇒ k = 4

Thus, the correct answer is 4 days.