Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 10)
10.
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
Answer: Option
Explanation:
| (P + Q + R)'s 1 hour's work = |  |
1 | + | 1 | + | 1 |  |
= | 37 | . |
| 8 | 10 | 12 | 120 |
| Work done by P, Q and R in 2 hours = | |
37 | x 2 | |
= | 37 | . |
| 120 | 60 |
| Remaining work = | |
1 - | 37 | |
= | 23 | . |
| 60 | 60 |
| (Q + R)'s 1 hour's work = | |
1 | + | 1 | |
= | 11 | . |
| 10 | 12 | 60 |
| Now, | 11 | work is done by Q and R in 1 hour. |
| 60 |
| So, | 23 | work will be done by Q and R in | |
60 | x | 23 | |
= | 23 | hours  2 hours. |
| 60 | 11 | 60 | 11 |
So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.
Discussion:
96 comments Page 8 of 10.
Vachu said:
1 decade ago
Why p is working for two hrs its ont mentioned?
Jyothi.k said:
1 decade ago
@Sowjanya
11/60 work done by q and r in i hour
Therefore
1 work done by q and r in 60/11 hour
So 23/60 work done by q and r in 60/11*23/60 hours
11/60 work done by q and r in i hour
Therefore
1 work done by q and r in 60/11 hour
So 23/60 work done by q and r in 60/11*23/60 hours
Pandu said:
1 decade ago
This problem code is length. Please any shortcut of this problem.
Ankit Jha said:
1 decade ago
I did it other way around.
2*(P+Q+R)'s 1 hour work + (Q+R)'s 1 hour work*X = 1.
37/60+(1/10+1/12)*x = 1.
11/60*x = 23/60.
x = 23/11 which is approximately equal to 2.
Hence Total time taken would be the initial two hours where P also contributed and the rest 23/11 i.e. 2 hours where only Q and are contributed.
Therefore, Total time will be 2+2= 4 Hours.
9:00 AM + 4 hours will be 1:00 PM.
Corrections are most welcome.
2*(P+Q+R)'s 1 hour work + (Q+R)'s 1 hour work*X = 1.
37/60+(1/10+1/12)*x = 1.
11/60*x = 23/60.
x = 23/11 which is approximately equal to 2.
Hence Total time taken would be the initial two hours where P also contributed and the rest 23/11 i.e. 2 hours where only Q and are contributed.
Therefore, Total time will be 2+2= 4 Hours.
9:00 AM + 4 hours will be 1:00 PM.
Corrections are most welcome.
Sowjanya said:
1 decade ago
Hey friends. Can any one suggest why 60/11 is multiplied with 23/60?
Akash said:
9 years ago
100000 books
P = 8h.
Q = 10h.
R = 12h.
No of books in 1h:
P = 100000/8 = 12500.
Q = 100000/10 = 10000.
R = 100000/12 = 8333.3.
9am to 11am = 2 hrs
In 2 hrs:
P = 25000.
Q = 20000.
R = 16666.6.
P + Q + R = 61666.6.
LEFT = 100000 - 61666.6 = 38333.4.
After 1h Q + R = 18333.3.
LEFT = 20000.
Again After 1h Q + R = 18333.3.
Approximately at 1pm.
P = 8h.
Q = 10h.
R = 12h.
No of books in 1h:
P = 100000/8 = 12500.
Q = 100000/10 = 10000.
R = 100000/12 = 8333.3.
9am to 11am = 2 hrs
In 2 hrs:
P = 25000.
Q = 20000.
R = 16666.6.
P + Q + R = 61666.6.
LEFT = 100000 - 61666.6 = 38333.4.
After 1h Q + R = 18333.3.
LEFT = 20000.
Again After 1h Q + R = 18333.3.
Approximately at 1pm.
Gautham Raj said:
9 years ago
It's very clear now thank you all for explaining this.
Revathi Yadavalli said:
9 years ago
Hi,
I did this solution as follows any one tell to me its right or wrong.
P = 1L - 8Hrs.
Q = 1L - 10Hrs.
R = 1L = 12Hrs.
The time difference between P, Q, R is 2hrs only.
So,
P Work starts 9AM And Finished it 11AM.
Q Work starts 9AM And Finished it 13PM (11+2).
R Work starts 9AM And Finished it 15PM (13+2).
I did this solution as follows any one tell to me its right or wrong.
P = 1L - 8Hrs.
Q = 1L - 10Hrs.
R = 1L = 12Hrs.
The time difference between P, Q, R is 2hrs only.
So,
P Work starts 9AM And Finished it 11AM.
Q Work starts 9AM And Finished it 13PM (11+2).
R Work starts 9AM And Finished it 15PM (13+2).
Sundar said:
10 years ago
Hi, I did it in a way can anyone tell me its right or not.
p = 8, q = 10, r = 12.
Thus, the ratio is 4:5:6.
Work starts at 9.00am and p finish at 11am.
Thus, q can be 12pm and c can be 13pm then the average time will be 13pm, it's 1pm.
Did my assumption is correct? Please give me a suggestion.
p = 8, q = 10, r = 12.
Thus, the ratio is 4:5:6.
Work starts at 9.00am and p finish at 11am.
Thus, q can be 12pm and c can be 13pm then the average time will be 13pm, it's 1pm.
Did my assumption is correct? Please give me a suggestion.
Res said:
10 years ago
How you consider 1hr for (Q + R).
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