Grace is twice as efficient as Garry and Garry is thrice as efficient as Guna,…
2025
Grace is twice as efficient as Garry and Garry is thrice as efficient as Guna, who can finish a job alone in 24 days. If Grace, Garry and Guna work on alternate days with Grace starting first, in how many days will the job finish?
- A.
6 1/2 days
- B.
7 1/2 days
- C.
6 2/3 days
- D.
7 days
Attempted by 25 students.
Show answer & explanation
Correct answer: C
Solution: Find each person’s daily work, compute work done in cycles, then determine the remaining time.
Guna alone finishes the job in 24 days, so Guna's rate = 1/24 job per day.
Garry is thrice as efficient as Guna, so Garry's rate = 3 × 1/24 = 1/8 job per day.
Grace is twice as efficient as Garry, so Grace's rate = 2 × 1/8 = 1/4 job per day.
They work alternately starting with Grace: in each 3-day cycle (Grace + Garry + Guna) they do 1/4 + 1/8 + 1/24 = 5/12 of the job.
After two full cycles (6 days) they complete 2 × 5/12 = 5/6 of the job, leaving 1/6 remaining.
On the next day Grace works at rate 1/4 per day, so time to finish the remaining 1/6 is (1/6) ÷ (1/4) = 2/3 day.
Total time = 6 days + 2/3 day = 6 2/3 days.