Two persons X and Y can do a piece of work in n days. If X alone can complete…
2023
Two persons X and Y can do a piece of work in n days. If X alone can complete the work in (n+3) days and Y alone can do the work in (n+12) days, find the value of n.
Answer: A. 6 — CONCEPTFor a fixed amount of work, a person’s one-day work rate is the reciprocal of the number of days that person takes alone. When two people work…
- A.
6
- B.
10
- C.
7
- D.
5
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Show answer & explanation
Correct answer: A
CONCEPT
For a fixed amount of work, a person’s one-day work rate is the reciprocal of the number of days that person takes alone.
When two people work together, their individual rates are added; the reciprocal of the combined rate is their joint completion time.
APPLICATION
Let the total work be 1 unit. X’s rate is 1/(n+3), Y’s rate is 1/(n+12), and their joint rate is 1/n.
Equate the sum of the individual rates to the joint rate: 1/(n+3) + 1/(n+12) = 1/n.
Multiply by n(n+3)(n+12): n(n+12) + n(n+3) = (n+3)(n+12).
Expand both sides: 2n2 + 15n = n2 + 15n + 36.
Subtract n2 + 15n from both sides: n2 = 36.
Since a completion time must be positive, n = 6 days.
CROSS-CHECK
For n = 6, X takes 9 days and Y takes 18 days. Their combined rate is 1/9 + 1/18 = 1/6, so together they take 6 days.
Therefore, n = 6.