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:
95 comments Page 7 of 10.
Vikash said:
1 decade ago
What about the 0.09 hr left in the answer which doesn't add to the answer?
Rekha Muragod said:
1 decade ago
Here no need of lengthy calculations.
Just look at time taken by each machine P will takes 8 hrs and Q takes 10 hrs, are takes 12 hrs.
So the common time difference between all 3 machines is = 2 hrs.
So just add this time to P's close time.
11 am+2 = 1 pm.
That's it.
Just look at time taken by each machine P will takes 8 hrs and Q takes 10 hrs, are takes 12 hrs.
So the common time difference between all 3 machines is = 2 hrs.
So just add this time to P's close time.
11 am+2 = 1 pm.
That's it.
Zoya said:
1 decade ago
Why we multiplying total time (x) by 1/8, 1/10, 1/12?
Why here we doing x/8+1/10+1/12?
Is there any formula like total time/work done?
Please anyone help me for this method.
Why here we doing x/8+1/10+1/12?
Is there any formula like total time/work done?
Please anyone help me for this method.
K.anusha said:
1 decade ago
Please I can't get the answer this last step please friends will explain to me.
How will come to this is 3/4 can you explain to me friends please.
How will come to this is 3/4 can you explain to me friends please.
Hariteja said:
1 decade ago
Hey guys I used a logic mite be correct or not I don't know!
As we know p works for 8hrs, q works for 10hrs and are works for 12hrs so there is difference of 2hrs. Where p complete the works for only 2hrs in time 9am to 11am. In the same time the remaining q and are also works but we observe by comparing q works more than 2hrs so if the q started at the same time where p started then q finish the work at 11am but where as are who work for 4hrs more than p. So in the time of he started he also completes the work at 11am but remaining 2hrs he need to work so the work will be finished at 1pm i.e. (11am+2hrs).
As we know p works for 8hrs, q works for 10hrs and are works for 12hrs so there is difference of 2hrs. Where p complete the works for only 2hrs in time 9am to 11am. In the same time the remaining q and are also works but we observe by comparing q works more than 2hrs so if the q started at the same time where p started then q finish the work at 11am but where as are who work for 4hrs more than p. So in the time of he started he also completes the work at 11am but remaining 2hrs he need to work so the work will be finished at 1pm i.e. (11am+2hrs).
Ranjeet singh said:
1 decade ago
A+B+C = 3/25.
A+A = 3/25 //B+C = A.
2A = 3/25.
A = 3/25*2.
A = 3/50.
A+A = 3/25 //B+C = A.
2A = 3/25.
A = 3/25*2.
A = 3/50.
Shobith said:
1 decade ago
That total of "1" represents the one day.
In the step 2*1/8+(1/80)*x+(1/12)x = 1.
Right @Sameer.
In the step 2*1/8+(1/80)*x+(1/12)x = 1.
Right @Sameer.
Sini said:
1 decade ago
Written by @Sameer:
P 1hrs work 1/8.
Q 1hrs work 1/10.
R 1hrs work 1/12.
p worked for 2 hrs so 2*1/8.
Suppose Q and r worked for 'x' hrs.
then,
2*1/8+(1/10)*x+(1/12)x = 1.
x=4.09.
Ans 9+4.09 = 1pm.
Sameer, How do we get the step 2*1/8+(1/10)*x+(1/12)x = 1.
i.e how is the total equal to 1?
P 1hrs work 1/8.
Q 1hrs work 1/10.
R 1hrs work 1/12.
p worked for 2 hrs so 2*1/8.
Suppose Q and r worked for 'x' hrs.
then,
2*1/8+(1/10)*x+(1/12)x = 1.
x=4.09.
Ans 9+4.09 = 1pm.
Sameer, How do we get the step 2*1/8+(1/10)*x+(1/12)x = 1.
i.e how is the total equal to 1?
SANJEEV said:
1 decade ago
2(1/8)+x(1/10 + 1/12) = 1.
>> x=45/11 nearly 4 >> 1pm.
>> x=45/11 nearly 4 >> 1pm.
Vasanthakumaran P said:
1 decade ago
Hi Friends,
1) P worked from 9 AM to 11 AM (2 hours of work time).
2) In two hours it can print 25,000 books ( Since, 100,000 books in 8 hours it can Print)
3) So remaining 75000 books has to be printed by other two machines (Q and R).
4) Compute the capacity of Q and R, viz : Q+R = ((1/10)+(1/12))= 11/60 = 5.45 hours.
5) So lets put ourself a question. Both the machine needs 5.45 hours to Print 100,000 books. But already 25,000 books has been printed by Machine P. To print remaining 75,000 books Q and R will be needing approximately 4 hours.
Viz; Let x be the number of hours required by Q and R to print 75,000 books.
x = [(5.45*75,000)/100,000] = 4 hours (approximately).
6) All the machines started at 9 Am. Hence 9 + 4 = 13 (1.00 pm).
1) P worked from 9 AM to 11 AM (2 hours of work time).
2) In two hours it can print 25,000 books ( Since, 100,000 books in 8 hours it can Print)
3) So remaining 75000 books has to be printed by other two machines (Q and R).
4) Compute the capacity of Q and R, viz : Q+R = ((1/10)+(1/12))= 11/60 = 5.45 hours.
5) So lets put ourself a question. Both the machine needs 5.45 hours to Print 100,000 books. But already 25,000 books has been printed by Machine P. To print remaining 75,000 books Q and R will be needing approximately 4 hours.
Viz; Let x be the number of hours required by Q and R to print 75,000 books.
x = [(5.45*75,000)/100,000] = 4 hours (approximately).
6) All the machines started at 9 Am. Hence 9 + 4 = 13 (1.00 pm).
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