Multiple choice

Ayesha, Rohan, and Kabir are assigned a painting project. Ayesha can complete the project alone in 30 days, Rohan in 24 days, and Kabir in 40 days. Rohan works on the project daily. Ayesha works only on alternate days beginning from Day 1, while Kabir assists only on alternate days starting from Day 2. On which day will the project be completed?

  1. 12th day

  2. 13th day

  3. 14th day

  4. 15th day
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Ayesha rate = 1/30, Rohan = 1/24, Kabir = 1/40. Day 1: A+R = 1/30 + 1/24 = 9/120 = 3/40. Day 2: R+K = 1/24 + 1/40 = 8/120 = 1/15. Cycle of 2 days = 3/40 + 1/15 = 17/120. In 14 days (7 cycles), work done = 7 * 17/120 = 119/120. Remaining 1/120 on Day 15 by A+R, which is enough.

AI explanation

Using the least common multiple method, let the total work be 120 units. The daily work capacities are Ayesha at 4 units, Rohan at 5 units, and Kabir at 3 units. On the first day, Ayesha and Rohan complete 9 units, and on the second day, Rohan and Kabir complete 8 units, making the two-day work output 17 units. In 14 days, which is 7 full cycles, they complete 119 units of work. On the 15th day, the remaining 1 unit of work is completed, so the project finishes on the 15th day.

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