P works 25% more efficiently than Q and Q works...

[BTGmoderatorLU]

P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project , P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 125 days, in how many days can R alone complete the remaining work?

A. 50 days
B. 75 days
C. 100 days
D. 150 days
E. 80 days

The OA is B.

I'm confused with this PS question. Experts, any suggestion about how to solve it? Thanks in advance.

[Scott@TargetTestPrep]

P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project , P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 125 days, in how many days can R alone complete the remaining work?

A. 50 days
B. 75 days
C. 100 days
D. 150 days
E. 80 days

The OA is B.

We can let x = the number of days it takes R alone to complete the entire project. So R's rate is 1/x, and therefore, Q's rate is 1.5(1/x) = 1.5/x = 3/2x and P's rate is 1.25(3/2x) = 5/4(3/2x) = 15/8x.

Since P alone takes 50 days less than Q alone to complete the entire project, we can determine the value of x using the equation:

1/(15/8x) = 1/(3/2x) - 50

8x/15 = 2x/3 - 50

Multiplying the equation by 15, we have:

8x = 10x - 750

750 = 2x

375 = x

So, R's rate is 1/375, Q's rate is 3/(2 * 375) = 3/750 = 1/250, and P's rate is 15/(8 * 375) = 15/300 = 1/200. Now, we can let n = the number of days it takes R alone to complete the remaining work (after P alone works for 60 days and Q alone works for 125 days) and create the equation:

60 * 1/200 + 125 * 1/250 + n * 1/375 = 1

3/10 + 1/2 + n/375 = 1

n/375 = 1/5

5n = 375

n = 75

Answer: B