Time and Work problems
- 1. Two pipes A and B can each fill a tank in 40 and 60 min, respectively. There is an outlet C. If all the 3 pipes are opened up, the tank will be filled in 30 min. How much time will it take for C alone to empty the full tank?
Options- A. 1 h
- B. 2 h
- C. 3 h
- D. 4 h Discuss
Correct Answer: 2 h
Explanation:
Work done by C in one min = (1/40 + 1/60) - 1/30 = 1/120
Hence, C can empty the tank in 120 min or 2 h.
- 2. A conveyer belt delivers baggage at the rate of 3 tonne in 5 min and a second conveyer belt delivers baggage at the rate of 1 tonne in 2 min. How much time will it take to get 33 tonne of baggage using both conveyer belts?
Options- A. 25 min and 30 s
- B. 30 min
- C. 35 min
- D. 40 min and 45 s Discuss
Correct Answer: 30 min
Explanation:
The weight of baggage deliver in 1 min by 1st belt = 3/5 tonne
The weight of baggage deliver in 1 min by 2nd belt = 1/2 tonne
The weight of baggage deliver in 1 min by both belt = 3/5 + 1/2 = 11/10 tonne
So, the two belts delivers 1 tonne in 10/11 min.
Hence, required time to deliver 33 tonne = (10/11) x 33 = 30 min
- 3. Rohit, Harsh and Sanjeev are three typists, who working simultaneously, can type 216 pages in four hours . In one hour, Sanjeev can type as many pages more than Harsh as Harsh can type more than Rohit. During a period of five hours, Sanjeev can type as many passages as Rohit can, during seven hours. How many pages does each of them type per hour?
Options- A. 16, 18, 22
- B. 14, 17, 20
- C. 15, 17, 22
- D. 15, 18, 21 Discuss
Correct Answer: 15, 18, 21
Explanation:
Let Rohit, Harsh and Sanjeev can type x, y and z pages respectively in 1 h.
Therefore, they together can type 4(x + y + z) pages in 4 h
? 4(x + y + z) = 216
? x + y + z = 54 .....(i)
Also, z - y = y - x
i.e., 2y = x + z ......(ii)
From Eqs. (i) and (ii), we get
3y = 54
? y = 18
From Eq. (ii), x + z = 36 ....(iv)
From Eqs. (iii) and (iv),
we get x = 15 and z = 21
- 4. A and B together can do a piece of work in 12 days which B and C together can do in 16 days. After A has been working at it for 5 days and B for 7 days, C takes up and finishes it alone in 13 days. In how many days, C alone can do the work?
Options- A. 16 days
- B. 32 days
- C. 24 days
- D. 48 days Discuss
Correct Answer: 24 days
Explanation:
(A + B)'s one day work = 1/12
(B + C)'s one day work = 1/16
Now, from the question,
A's 5 days work + B's 7 days work + C's 13 days work = 1
? A's 5 days work + B's 5 days work + B's 2 days work + C's 2 days work + C's 11 days work = 1
(A + B)'s 5 days work + (B + C)'s 2 days work + C's 11 days work = 1
? 5/12 + 2/16 + C's 11 days work = 1
? C's 11 days work = 1 - (5/12 + 2/16) = 11/24
? C's 1 day work = (11/24) x 11 = 1/24
Hence, C can do this work in 24 days.
- 5. A and B can complete a piece of work in 12 days while B and C in 15 days. A did the work for 3 days, B for 8 days and C for 10 days to complete the work. In how many days C alone can complete the work?
Options- A. 10 days
- B. 11 days
- C. 12 days
- D. 14 days Discuss
Correct Answer: 12 days
Explanation:
Fraction of work complete by (A and B) + Fraction of work complete by (B and C) + Fraction of work completed by C = 1
As B did the work for 8 days we can say B did the work for 3 days with A and B did the work for 5 days with C. So, A and B together did the work for 3 days, B and C together did the work for 5 days, C alone did the work for 5 days.
? 3/12 + 5/15 + 5/x = 1 or 5/x = 5/12
i.e., x = 12 or C alone can complete the work in 12 days
- 6. A supplies 20 men who work for 8 h per days for 6 days. B supplies 15 men working at 9 h per day for 7 day and C supplies 10 men working 6 h per day for 8 days to do a certain lob. If ? 636 is paid for all the labour, what is C's share?
Options- A. ? 128
- B. ? 136
- C. ? 148
- D. ? 154 Discuss
Correct Answer: ? 128
Explanation:
Total man hours work done by men supplied by A, B and C
= (20 x 8 x 6), (15 x 9 x 7), (10 x 6 x 8) and the wages must be in the ratio of the work done.
So, ? 636 has to divided among A, B and C in the ratio (20 x 8 x 6) : (15 x 9 x 7) : (10 x 6 x 8) = 64 : 63 : 32
? C's share = (32/159) x 636 = ? 128
- 7. A and B can do a piece of work in 45 days and 40 days, respectively. They began to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days after which A left the work, is?
Options- A. 7 days
- B. 8 days
- C. 9 days
- D. 10 days Discuss
Correct Answer: 9 days
Explanation:
By the fundamental of work and time,
x/45 + (x + 23)/40 = 1
? x = 9 days
- 8. 50 men or 80 women can finish a job in 50 days. A contractor deploys 40 men and 48 women for this work but after every duration of 10 days, 5 men and 8 women are removed till the work is completed. The work is completed in?
Options- A. 45 days
- B. 50 days
- C. 54 days
- D. 62 days Discuss
Correct Answer: 50 days
Explanation:
Since, 50 men can do a job in 50 days.
So, work done by 1 man in a day = 1/(50 x 50)
Also, 80 women can do the job in 50 days.
So, work done by 1 women in 1 day = 1/(50 x 80)
Now, work done by 40 men and 48 women in first 10 days
= (40 x 10)/(50 x 50) + (48 x 10)/(50 x 80)
= 4/25 + 3/25 = 7/25
Now, 5 men and 8 women are removed after 10 days,
So work done by 35 men and 40 women in 10 days = (35 x 10)/(50 x 50) + (40 x 10)/(50 x 80)
= 7/50 + 1/10 = (7 + 5)/50
= 6/25
Again, 5 men and 8 women are removed after 10 days,
So work done by 30 men and 32 women in 10 days = (30 x 10)/(50 x 50) + (32 x 10)/(50 x 80) = 5/25
Now, after every 10 days as the number of men and
women decrease, work done also decreased by 1/25th past.
So, work done after every 10 days upto 50 days = 7/25 + 6/25 + 5/25 + 4/25 + 3/25
= 25/25 = 1
So, it will take 50 days for them to complete the work.
- 9. 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 day work = 50%
B's 5 day work = 33.33%
C's 2 day work = 16.66% [100 - (50 + 33.33)]
Ratio of contribution of work of A , B and C = 50 : 33.33 : 16.66 = 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
and C's one day's earning = Rs. 250
- 10. Efficiency of Asha is 25% more then Usha and Usha takes 25 days to complete a piece of work. Asha started a work alone and then usha joined her 5 days before actual completion of the work. For how many days Asha worked alone?
Options- A. 9
- B. 11
- C. 10
- D. 15 Discuss
Correct Answer: 11
Explanation:
Efficiency (Asha : Usha) = 5 : 4
Number of days(Asha : Usha) = 4x : 5x = 4x : 25
? Number of days required by Asha to finish the work alone = 4x
= 4 x 5 = 20.
Now, since Asha and Usha did work together for last 5 days = 5 x 9 = 45%
(since efficiency of Asha = 5% and Usha's efficiency = 4%)
It means Asha completed 55% work alone.
? No. of days taken by Asha to complete 55% work = 55/5 = 11days
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