Multiple choice

X, Y and Z individually do a job in 24, 30 and 40 days, respectively. X works alone for the 1st day, then Y works alone for next 2 days and then Z works alone for next 3 days. The same pattern is repeated. In how many days will the job be finished?

  1. 32

  2. 32.7

  3. 64.5

  4. 32.25

  5. 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rates: X=1/24, Y=1/30, Z=1/40. Work per cycle (6 days): 1*(1/24) + 2*(1/30) + 3*(1/40) = 1/24 + 1/15 + 3/40 = (5+8+9)/120 = 22/120 = 11/60. In 5 cycles (30 days), work = 55/60. Remaining 5/60 = 1/12. Day 31: X does 1/24. Day 32: Y does 1/30. Remaining work = 1/12 - 1/24 - 1/30 = 1/24 - 1/30 = 1/120. Day 33: Z does 1/40. Time = 32 + (1/120)/(1/40) = 32 + 1/3 = 32.33. The closest option is 32.25.

AI explanation

The Least Common Multiple of 24, 30 and 40 is 120, so let the total work be 120 units. The daily efficiencies for X, Y and Z are 5, 4 and 3 units, respectively. In one 6-day cycle, the work done is 5 + (4 * 2) + (3 * 3) = 22 units. Five such cycles complete 110 units in 30 days, leaving 10 units of work for the 31st day. On the 31st day, X works alone and completes 5 units, leaving 5 units. Y then works alone on the 32nd and 33rd days to complete the remaining 5 units at 4 units per day, taking 1.25 days. The total time taken is 32.25 days.

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