Time and Work problems
- 1. Rashmi can do a piece of work in 16 days. Ravina can do the same work in 12 4/ 5 days, while Gitika can do it in 32 days. All of them started to work together but Rashmi leaves after 4 days. Ravina leaves the job 3 days before the completion of the work. How long would the work last?
Options- A. 9 days
- B. 6 days
- C. 18 days
- D. 5 days Discuss
Correct Answer: 9 days
Explanation:
Let the work lasted for N days,
Then, Rashmi's 4 day's work + Ravina (N - 3) day's + Gitika's N day's work = 1
? (4/16) + (N - 3) / (124/5) + N/32 = 1
? 5(N - 3)/64 + N/32 = 1 - 1/4
? [5(N - 3) + 2N] / 64 = 3/4
? 7N - 15 = 48
? N= (48 + 15)/7 = 63/7 = 9 days
- 2. A can do a piece of work in 10 days, B in 15 days. They work together for 5 days, the rest of the work is finished by C in two more days. If they get Rs. 3000 as wages for the whole work, what are the daily wages of A, B and C respectively (in Rs):
Options- A. 200, 250, 300
- B. 300, 200, 250
- C. 200, 300, 400
- D. None of these Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 300, 200, 250
Explanation:
A's 5 days work = 50%
B's 5 days work = 33.33%
C's 2 days work = 16.66% [100- (50+33.33)]
Ratio of contribution of work of A, B and C = = 3 : 2 : 1
A's total share = Rs. 1500
B's total share = Rs. 1000
C's total share = Rs. 500
A's one day's earning = Rs.300
B's one day's earning = Rs.200
C's one day's earning = Rs.250
- 3. A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
Options- A. 11 days
- B. 12 days
- C. 13 days
- D. 14 days Discuss
Correct Answer: 11 days
Explanation:
One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10.
C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.
Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10.
Remaining Work = 7/10, which was done by A,B and C in the initial number of days.
Number of days required for this initial work = 7 days.
Thus, the total numbers of days required = 4 + 7 = 11 days.
- 4. 12 men can complete a work in 8 days. 16 women can complete the same work in 12 days. 8 men and 8 women started working and worked for 6 days. How many more men are to be added to complete the remaining work in 1 day?
Options- A. 8
- B. 12
- C. 16
- D. 24 Discuss
Correct Answer: 12
Explanation:
1 man's 1 day work =1/96 ; 1 woman's 1 day work = 1/192
Work done in 6 days=
Remaining work = 1/4
(8 men +8 women)'s 1 day work = =1/8
Remaining work =1/4 - 1/8 = 1/8
1/96 work is done in 1 day by 1 man
Therefore, 1/8 work will be done in 1 day by 96 x (1/8) =12 men
- 5. P can complete a work in 12 days working 8 hours a day.Q can complete the same work in 8 days working 10 hours a day. If both p and Q work together,working 8 hours a day,in how many days can they complete the work?
Options- A. 60/11
- B. 61/11
- C. 71/11
- D. 72/11 Discuss
Correct Answer: 60/11
Explanation:
P can complete the work in (12 x 8) hrs = 96 hrs
Q can complete the work in (8 x 10) hrs=80 hrs
Therefore, P's 1 hour work=1/96 and Q's 1 hour work= 1/80
(P+Q)'s 1 hour's work =(1/96) + (1/80) = 11/480. So both P and Q will finish the work in 480/11 hrs
Therefore, Number of days of 8 hours each = (480/11) x (1/8) = 60/11
- 6. A and B can do a piece of work in 30 days , while B and C can do the same work in 24 days and C and A in 20 days . They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
Options- A. 18 days
- B. 24 days
- C. 30 days
- D. 36 days Discuss
Correct Answer: 18 days
Explanation:
2(A+B+C)'s 1 day work = 1/30 + 1/24 + 1/20 = 1/8
=>(A+B+C)'s 1 day's work= 1/16
work done by A,B and C in 10 days=10/16 = 5/8
Remaining work= 3/8
A's 1 day's work=
Now, 1/48 work is done by A in 1 day.
So, 3/8 work wil be done by A in =48 x (3/8) = 18 days
- 7. A can do a certain work in the same time in which B and C together can do it.If A and B together could do it in 20 days and C alone in 60 days ,then B alone could do it in:
Options- A. 20days
- B. 40 days
- C. 50 days
- D. 60 days Discuss
Correct Answer: 60 days
Explanation:
(A+B)'s 1 day's work=1/20
C's 1 day work=1/60
(A+B+C)'s 1 day's work= 1/20 + 1/60 = 1/15
Also A's 1 day's work =(B+C)'s 1 day's work
Therefore, we get: 2 x (A's 1 day 's work)=1/15
=>A's 1 day's work=1/30
Therefore, B's 1 day's work= 1/20 - 1/30 = 1/60
So, B alone could do the work in 60 days.
- 8. A works twice as fast as B.If B can complete a work in 18 days independently,the number of days in which A and B can together finish the work is:
Options- A. 4 days
- B. 6 days
- C. 8 days
- D. 10 days Discuss
Correct Answer: 6 days
Explanation:
Ratio of rates of working of A and B =2:1. So, ratio of times taken =1:2
Therefore, A's 1 day's work=1/9
B's 1 day's work=1/18
(A+B)'s 1 day's work= 1/9 + 1/18 = 1/6
so, A and B together can finish the work in 6 days
- 9. A Contractor employed a certain number of workers to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?
Options- A. 10 %
- B. 14 ( 2/7 )%
- C. 20 %
- D. Can't be determined Discuss
Correct Answer: 14 ( 2/7 )%
Explanation:
Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.
D * x +(100- D) * 2x= 175x
=> D= 25 days
Now , the work done in 25 days = 25x
Total work = 175x
Therefore, workdone before increasing the no of workers = % =
- 10. A,B,C together can do a piece of work in 10 days.All the three started workingat it together and after 4 days,A left.Then,B and C together completed the work in 10 more days.In how many days can complete a work alone ?
Options- A. 25
- B. 24
- C. 23
- D. 21 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 25
Explanation:
(A+B+C) do 1 work in 10 days.
So (A+B+C)'s 1 day work=1/10 and as they work together for 4 days so workdone by them in 4 days=4/10=2/5
Remaining work=1-2/5=3/5
(B+C) take 10 more days to complete 3/5 work. So( B+C)'s 1 day work=3/50
Now A'S 1 day work=(A+B+C)'s 1 day work - (B+C)'s 1 day work=1/10-3/50=1/25
A does 1/25 work in in 1 day
Therefore 1 work in 25 days.
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