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
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