Select the correct answerA work can be completed by P and Q in 12 days, Q and R in 15 days, R and P in 20 days. In how many days alone P can finish the work?Options10 days30 days60 days20 days
Question
Select the correct answerA work can be completed by P and Q in 12 days, Q and R in 15 days, R and P in 20 days. In how many days alone P can finish the work?Options10 days30 days60 days20 days
Solution
To solve this problem, we need to find the rates at which P, Q, and R work.
- P and Q can complete the work in 12 days, so their combined rate is 1/12 of the work per day.
- Q and R can complete the work in 15 days, so their combined rate is 1/15 of the work per day.
- R and P can complete the work in 20 days, so their combined rate is 1/20 of the work per day.
If we add these three rates together, we get (1/12 + 1/15 + 1/20) = 1/4 of the work per day. But this is twice the sum of the rates of P, Q, and R (because each is counted twice in the sum), so the sum of the rates of P, Q, and R is (1/4)/2 = 1/8 of the work per day.
If we subtract the rates of Q and R from this, we can find the rate of P:
The rate of Q and R is 1/15 of the work per day, so the rate of P is (1/8 - 1/15) = 7/120 of the work per day.
Therefore, P can complete the work alone in 120/7 days, which is approximately 17.14 days.
However, this is not one of the options given. It seems there may be a mistake in the problem or the options provided.
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