Arithmetic

Time & Work

Medium

A and B can complete a job in 24 days working together. A alone can complete it in 32 days. Both of them worked together for 8 days and then A left. The number of days B will take to complete the remaining job is:

128 days

64 days

32 days

16 days

✅ Correct Option: 2

A and B together complete the job in 24 days, so their combined rate is $\frac{1}{24}$ of the job per day.

A alone completes the job in 32 days, so A's rate is $\frac{1}{32}$ of the job per day.

B's rate = (A and B together) - (A alone)

$B's \ rate = \frac{1}{24} - \frac{1}{32}$

Finding common denominator (LCM of 24 and 32 is 96):

$= \frac{4}{96} - \frac{3}{96}$

$= \frac{1}{96}$ of job per day

Therefore, B alone takes 96 days to complete the full job.

Both A and B worked together for 8 days.

$Work \ done = \frac{1}{24} \times 8$

$= \frac{8}{24}$

$= \frac{1}{3}$

They completed $\frac{1}{3}$ of the job in 8 days.

$Remaining \ work = 1 - \frac{1}{3}$

$= \frac{2}{3}$

B works alone on the remaining work. B's rate is $\frac{1}{96}$ per day.

$Time = \frac{2}{3} \div \frac{1}{96}$

$= \frac{2}{3} \times 96$

$= \frac{192}{3}$

$= 64$ days

Therefore, B will take 64 days to complete the remaining job.

2025: 13 May Shift 1

P and Q can complete a job in 24 days working together. P can alone complete it in 32 days. Both of them worked together for 8 days and then P left. The number of days Q will take to complete the remaining job is:

2025: 26 May Shift 1

A can complete a work in 16 days, working 6 hours a day. B can complete the same work in 12 days, working 9 hours a day. If both A and B work together, working 8 hours a day, in how many days can they complete the work?

2025: 3 June Shift 2

P and Q can do work separately in 10 and 20 days, respectively. In how many days can they finish it, working together?

2025: 2 June Shift 2

30 boys are engaged to do a piece of work in 15 days but it is found that in 5 days, 3/5 work is completed. How many boys may be allowed to go off, so that the work may be finished on time?

2022: 6 Aug Shift 1

If 36 farmers can do a piece of work in 24 hours, In how many hours will 18 farmers do it?

2023: 11 June Shift 2

A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days that A alone will take to finish the work is:

A and B can complete a job in 24 days working together. A alone can complete it in 32 days. Both of them worked together for 8 days and then A left. The number of days B will take to complete the remaining job is:

Solution

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