P and Q can do a work in 10 days. Q and R can do it in 12 days. All three together can finish in 8 days. In how many days can P and R can complete the work?
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A.
10 days
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B.
8 days
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C.
12 days
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D.
15 days
Correct Answer:
@.
Explanation:
To find the time required for P and R to complete the work, we first determine the work rates of the individuals and groups involved. Let the total work be 120 units (the least common multiple of 8, 10, and 12).1. The combined rate of P, Q, and R is 120 / 8 = 15 units per day.
2. The combined rate of P and Q is 120 / 10 = 12 units per day.
3. The combined rate of Q and R is 120 / 12 = 10 units per day.To find the rate of R, subtract the P and Q rate from the total rate: 15 - 12 = 3 units per day.
To find the rate of P, subtract the Q and R rate from the total rate: 15 - 10 = 5 units per day.
The combined rate of P and R is 5 + 3 = 8 units per day. Therefore, P and R together can finish the 120 units of work in 120 / 8 = 15 days.
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