Three mechanics — Ravi, Sohail, and Karan — are assigned to repair a large machine. Working alone, Ravi can repair it in 9 days, Sohail can do the same in 18 days, and Karan can complete it alone in 12 days. They follow a rotating schedule: Ravi works on Day 1, Sohail on Day 2, Karan on Day 3, and then the cycle repeats in the same order (Ravi on Day 4, Sohail on Day 5, etc.). If they continue this pattern until the machine is fully repaired,
consider the following statements:
1. The repair will be finished on Day 10.
2. The repair will be finished by Karan.

Which of the above statements is/are correct?
(a) 1 only.
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

Question

Three mechanics &mdash; Ravi, Sohail, and Karan &mdash; are assigned to repair a large machine. Working alone, Ravi can repair it in 9 days, Sohail can do the same in 18 days, and Karan can complete it alone in 12 days. They follow a rotating schedule: Ravi works on Day 1, Sohail on Day 2, Karan on Day 3, and then the cycle repeats in the same order (Ravi on Day 4, Sohail on Day 5, etc.). If they continue this pattern until the machine is fully repaired,
 consider the following statements:
1. The repair will be finished on Day 10.
2. The repair will be finished by Karan.

Which of the above statements is/are correct?
(a) 1 only.
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

ONLiNE UPSC · Accepted Answer

Let total work = LCM (9, 18, 12) = 36 units
Ravi&rsquo;s rate = 36 &divide; 9 = 4 units/day
Sohail&rsquo;s rate = 36 &divide; 18 = 2 units/day
Karan&rsquo;s rate = 36 &divide; 12 = 3 units/day
Every 3-day cycle:
Ravi + Sohail + Karan = 4+2+3=94 + 2 + 3 = 94+2+3=9 units every 3 days
In 3 full cycles (9 days):
Work done = 3&times;9=273 &times; 9 = 273&times;9=27 units
Remaining = 36&minus;27=936 - 27 = 936&minus;27=9 unit
Day 10: Ravi&rsquo;s turn &rarr; does 4 units
Remaining = 5 units
Day 11: Sohail&rsquo;s turn &rarr; does 2 units
Remaining = 3 units
Day 12: Karan&rsquo;s turn &rarr; does 3 units
Remaining = 0
Final findings:
The work finishes on Day 12,
It is completed by Karan.

Hence, option b is correct.

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E Question 1	⏱ 0
Three mechanics — Ravi, Sohail, and Karan — are assigned to repair a large machine. Working alone, Ravi can repair it in 9 days, Sohail can do the same in 18 days, and Karan can complete it alone in 12 days. They follow a rotating schedule: Ravi works on Day 1, Sohail on Day 2, Karan on Day 3, and then the cycle repeats in the same order (Ravi on Day 4, Sohail on Day 5, etc.). If they continue this pattern until the machine is fully repaired, consider the following statements: 1. The repair will be finished on Day 10. 2. The repair will be finished by Karan. Which of the above statements is/are correct? (a) 1 only. (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2