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

BTGmoderatorLU wrote: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