x can do a piece of work in 20 days. he worked at it for 5 days and then y finished it in 15 days. in how many days can x and y together finish the work?
x can do a piece of work in 20 days. he worked at it for 5 days and then y finished it in 15 days. in how many days can x and y together finish the work?
Answer: Of course, here’s the solution presented in an organized manner:
Let’s assume the total work is 1 unit.
X’s efficiency = 1/20 (i.e., he can complete 1/20th of the work in 1 day)
Y’s efficiency = 1/15 (i.e., he can complete 1/15th of the work in 1 day)
X worked for 5 days, completing:
Work done by X = (1/20) * 5 = 1/4
Remaining work = 1 - 1/4 = 3/4
Y will finish the remaining work in 15 days, completing:
Work done by Y = (1/15) * 15 = 1
Let’s assume that X and Y together can finish the work in ‘d’ days. Their combined efficiency = 1/d.
Now, forming an equation based on the work done by X and Y together:
(1/20)*5 + (1/d)*d = 3/4
Simplifying the equation:
x/d = 9/20
So, d/x = 20/9
The number of days required for X and Y together to finish the work = x = (20/9)*d
Since Y can finish the remaining work in 15 days:
(1/15)*d = 3/4
Solving the equation: d = 45/4
Therefore, X and Y together can finish the work in:
x = (20/9)d = (20/9)(45/4) = 10 days
Hence, the correct answer is 10 days.