A completes a work in 3 days , B in 12 days ,C in 15 And D in 6 days. They…
2024
A completes a work in 3 days , B in 12 days ,C in 15 And D in 6 days. They form group of two such that difference is maximum between them to complete the work . What is difference in the number of days they complete that work?
- A.
15/4 days
- B.
14/3 days
- C.
11/2 days
- D.
12/3 days
Attempted by 14 students.
Show answer & explanation
Correct answer: B
Approach: Partition the four workers into two pairs and compute how many days each pair takes to finish the work together. Choose the partition with the largest difference between the two pair times.
Pairing: worker with 3 days and worker with 6 days. Combined rate = 1/3 + 1/6 = 1/2 → time = 2 days.
Pairing: worker with 12 days and worker with 15 days. Combined rate = 1/12 + 1/15 = 3/20 → time = 20/3 days.
Difference for this partition = 20/3 − 2 = 14/3 days.
Check the other possible partitions to confirm this is the maximum:
Partition: (3-day, 12-day) and (15-day, 6-day). Times = 12/5 days and 30/7 days → difference = 30/7 − 12/5 = 66/35 days (≈1.886).
Partition: (3-day, 15-day) and (12-day, 6-day). Times = 5/2 days and 4 days → difference = 4 − 5/2 = 3/2 days (1.5).
Answer: 14/3 days (obtained by pairing the 3-day worker with the 6-day worker, and pairing the 12-day worker with the 15-day worker).