P can lay railways track between two stations in 16 days. Q can do the same…
2023
P can lay railways track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they complete the job in 4 days. How much days does it take for R alone to complete the work ?
- A.
9(3/5) days
- B.
9(1/5) days
- C.
9(2/5) days
- D.
10 days
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Step-by-Step Solution
Identify Individual Work Rates:
P's rate of work = 1/16 of the job per day.
Q's rate of work = 1/12 of the job per day.
Combined rate of P, Q, and R = 1/4 of the job per day.
Calculate R's Work Rate:
R's rate = (Combined rate of P, Q, and R) - (P's rate + Q's rate).
R's rate = 1/4 - (1/16 + 1/12).
Find the least common multiple for 4, 16, and 12, which is 48.
R's rate = 12/48 - (3/48 + 4/48).
R's rate = 12/48 - 7/48 = 5/48 of the job per day.
Find Time Taken by R Alone:
Time = 1 / (Rate) = 1 / (5/48) = 48/5 days.
48/5 days = 9 and 3/5 days.