Multiple choice

A work can be completed by P and Q in 12 days. By Q and R in 15 days and by R and P in 20 days. In how many days can P alone finish the work completely ?

  1. 10 days

  2. 24 days

  3. 30 days

  4. 36 days

  5. 40 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P+Q=1/12, Q+R=1/15, R+P=1/20. Summing these: 2(P+Q+R) = 1/12 + 1/15 + 1/20 = (5+4+3)/60 = 12/60 = 1/5. So P+Q+R = 1/10. P = (P+Q+R) - (Q+R) = 1/10 - 1/15 = (3-2)/30 = 1/30. P takes 30 days.

AI explanation

Using the standard work equation, add the combined rates to get (1/P + 1/Q) + (1/Q + 1/R) + (1/R + 1/P) = 1/12 + 1/15 + 1/20. This simplifies to 2(1/P + 1/Q + 1/R) = 12/60, meaning the combined rate of all three is 1/10 of the work per day. Subtracting the rate of Q and R, which is 1/15, from the total combined rate gives P's individual rate as 1/10 minus 1/15, or 1/30. Therefore, P alone can finish the work in 30 days.

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