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15 Jan 2026, 04:00
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D
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Difficulty:
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Question Stats:
70% (02:26) correct
30%
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wrong
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Two persons, A and B, can each complete a job alone in 29 days. A rests for one day after every four days of work, and B rests for one day after every five days of work. If A and B start working together, how many days will it take to complete the job?
A. 12
B. 14
C. 15
D. 17
E. 18
A. 12
B. 14
C. 15
D. 17
E. 18
15 Jan 2026, 04:06
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assume total job 29 units. first 4 days both will work so 8 units.5th and 6th day one unit each. So every 6 days 10 units of work. 12 days 20 units done. 16 days- 20+8 units (both work)= 28 units. 17th day only B works, so 29 units will be completed
16 Jan 2026, 06:17
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Let the rate of work (W) done by A be represented by 'A' and that of B be 'B'
A = W/29 and B = W/29
To ease the calculation, let's assume the Work = LCM of the times taken by A and B = LCM(29,29) = 29
Thus, rate of work done by A per day = 1 and that of B = 1
Now, visualize the distribution of work done by A and B over a period of few days:
1st 2nd 3rd 4th 5th 6th
AB AB AB AB B A
This cycle would repeat till the work is completed. In one cycle, the work done = 2*4 + 1 + 1 = 10
Since the amount of work to be done = 29, we would require 2 such complete cycles and additional 9 units of work to be completed.
2 cycles = 2*6 days = 12 days
Till this point of time, 20 units of work is done and 9 are left.
Now, the cycle will again repeat -> AB AB AB AB B => 2+2+2+2+1 => 9 units (Hence, we would require an additional 5 days to get the entire work completed.
Hence, the total number of days = 12+5 = 17 days (Option D) (Ans)
A = W/29 and B = W/29
To ease the calculation, let's assume the Work = LCM of the times taken by A and B = LCM(29,29) = 29
Thus, rate of work done by A per day = 1 and that of B = 1
Now, visualize the distribution of work done by A and B over a period of few days:
1st 2nd 3rd 4th 5th 6th
AB AB AB AB B A
This cycle would repeat till the work is completed. In one cycle, the work done = 2*4 + 1 + 1 = 10
Since the amount of work to be done = 29, we would require 2 such complete cycles and additional 9 units of work to be completed.
2 cycles = 2*6 days = 12 days
Till this point of time, 20 units of work is done and 9 are left.
Now, the cycle will again repeat -> AB AB AB AB B => 2+2+2+2+1 => 9 units (Hence, we would require an additional 5 days to get the entire work completed.
Hence, the total number of days = 12+5 = 17 days (Option D) (Ans)
