Time and Work problems
- 1. M can complete a piece of work in 10 days. N is 33.33% less efficient than M. calculate the number of days required to both to complete the work?
Options- A. 6 days
- B. 8 days
- C. 11 days
- D. 13 days Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 6 days
Explanation:
M = 10 days
The ratio of efficiency of M & N are 3 : 2
Hence, the time rquired for N alone = 15 days
=> Required time taken t=by both to complete the work = M x N / M + N
= 10 x 15/ 10 + 15
= 150/25
= 6 days.
- 2. Four pipes P,Q, R and S can fill a cistern in 20,25, 40 and 50 hours respectively.The first pipe P was opened at 6:00 am, Q at 8:00 am, R at 9:00 am and S at 10:00 am. when will the Cistern be full?
Options- A. 4:18 pm
- B. 3:09 pm
- C. 12:15 pm
- D. 11:09 am Discuss
Correct Answer: 3:09 pm
Explanation:
Efficiency of P= 100/20= 5% per hour
Efficiency of Q= 100/25= 4% per hour
Efficiency of R= 100/40= 2.5% per hour
Efficiency of S=100/50= 2% per hour
Cistern filled till 10 am by P, Q and R
Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern.
Rest of cistern to be filled = 100 - 30.5 = 69.5%
Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern
= 69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx).
Therefore, total time =4 hrs + 5hrs 9 mins = 9 hrs and 9 mins
It means cistern will be filled up at 3:09 pm
- 3. P is 30% more efficient than Q. How much time will they, working together, take to complete a job which P alone could have done in 23 days?
Options- A. 16 days
- B. 13 days
- C. 15 days
- D. 12 days Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 13 days
Explanation:
Ratio of times taken by P & Q = 100 : 130 = 10:13
Let Q takes x days to do the work
Then, 10:13 :: 23:x
=> x = 23x13/10
=> x = 299/10
P's 1 day's work = 1/23
Q's 1 day's work = 10/299
(P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13
Hence, P & Q together can complete the work in 13 days.
- 4. 9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days ?
Options- A. 15 days
- B. 11 days
- C. 14 days
- D. 12 days Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 12 days
Explanation:
9M + 12B ----- 12 days ...........(1)
12M + 12B ------- 10 days........(2)
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B............(3)
From (1) & (3)
18B + 12B = 30B ---- 12 days
20B + 10B = 30B -----? => 12 days.
- 5. A contractor undertake to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work. How many men can be discharged so that the work may finish in time ?
Options- A. 64
- B. 62
- C. 58
- D. 56 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 56
Explanation:
Days remaining 124 ? 64 = 60 days
Remaining work = 1 - 2/3 = 1/3
Let men required men for working remaining days be 'm'
So men required = (120 x 64)/2 = (m x 60)/1 => m = 64
Men discharge = 120 ? 64 = 56 men.
- 6. Three athletes can complete one round around a circular field in 16, 24 and 36 min respectively. They start running together at same instant then after how much time they will meet to each other for first time ?
Options- A. 2 hrs 24 min
- B. 2 hrs 44 min
- C. 1 hrs 24 min
- D. 1 hrs 24 min Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 2 hrs 24 min
Explanation:
Given that three athletes can complete one round around a circular field in 16, 24 and 36 min respectively.
Now, required time after which they met for the first time = LCM of (16, 24 & 36) min
Now, LCM of 16, 24, 36 = 144 minutes = 2 hrs 24 min.
- 7. A contractor undertook a project to complete it in 20 days which needed 5 workers to work continuously for all the days estimated. But before the start of the work the client wanted to complete it earlier than the scheduled time, so the contractor calculated that he needed to increase 5 additional men every 2 days to complete the work in the time the client wanted it: If the work was further increased by 50% but the contractor continues to increase the 5 workers o every 2 days then how many more days are required over the initial time specified by the client.
Options- A. 1 day
- B. 2 days
- C. 5 days
- D. None of these Discuss
Correct Answer: 2 days
Explanation:
Total work = 100+50 = 150man-days
In 8 days 100 man-days work has been completed. Now on 9th and 10th day there will be 25 workers. So in 2 days they wll complete additional 50 man- days work. Thus the work requires 2 more days.
- 8. A can build a wall in 16 days while B can destroy it in 8 days. A worked for 5 days. Then B joined with A for the next 2 days. Find in how many days could A build the remaining wall ?
Options- A. 12 days
- B. 14 days
- C. 13 days
- D. 16 days Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 13 days
Explanation:
Now, Total work = LCM(16, 8) = 48
A's one day work = + 48/16 = + 3
B's one day work = - 48/8 = -6
Given A worked for 5 days to build the wall => 5 days work = 5 x 3 = + 15
2days B joined with A in working = 2(3 - 6) = - 6
Remaining Work of building wall = 48 - (15 - 6) = 39
Now this remaining work will be done by A in = 39/3 = 13 days.
- 9. A and B can do a piece of work for Rs 1540. Find the difference between the wages of C and B for the same work If A can do the work in 12 days and B can do the same work in 8 days and with the help of C, A and B can do the same work in 2 days?
Options- A. 980
- B. 1232
- C. 810
- D. 1121 Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 1232
Explanation:
From the given data,
Day Capacity
A -> 12 2
B -> 8 3 2
A + B + C -> 2 12
=> Capacity of C = 12 - 5 = 7
Ratio of capacity of A : B : C = 2 : 3 : 7
Difference of wages of C & B = 4/5 x 1540
= 4 x 308 = Rs. 1232
- 10. Time taken by P alone to finish a work is 50% more than the time taken by P and Q together. Q is thrice as efficient as R. If Q and R together can complete the work in 22.5 days, then how many days will P alone take to complete the work ?
Options- A. 17 days
- B. 11 days
- C. 15 days
- D. 16 days Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 15 days
Explanation:
We know that Time is inversely proportional to Efficiency
Here given time ratio of P & P+Q as
P/P+Q = 150/100 = 3:2
Efficiency ratio of P & Q as
P:Q = 2:1 ....(1)
Given Efficiency ratio of Q & R as
Q:R = 3:1 ....(2)
From (1) & (2), we get
P:Q:R = 6:3:1
P alone can finish the work in
22.5(3+1)/6 = 15 days.
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