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 8 of 10.
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).
Deepak said:
1 decade ago
A and B can done a work in 10 days, B and C done same work in 18 days,
If A did work 4 days, B did 8 days and C did 14 days. How much days C takes to complete same work?
If A did work 4 days, B did 8 days and C did 14 days. How much days C takes to complete same work?
Abhay said:
1 decade ago
A simple time saving shortcut :
P= 100000= 8hrs So Per hr work : 12500.
Q= 100000= 10 hrs So per hr work : 10000.
R =100000=12 hrs So Per hr : 8334.
9AM- 10 Am =12500+10000+8334=30834.
10 AM -11 Am = 30834 :: Total work completed: 30834+30834= 61668.
11AM-12PM = 61668+ 18334= 80002.
So definitely we require more time than 12PM. Just look at the option and click.
P= 100000= 8hrs So Per hr work : 12500.
Q= 100000= 10 hrs So per hr work : 10000.
R =100000=12 hrs So Per hr : 8334.
9AM- 10 Am =12500+10000+8334=30834.
10 AM -11 Am = 30834 :: Total work completed: 30834+30834= 61668.
11AM-12PM = 61668+ 18334= 80002.
So definitely we require more time than 12PM. Just look at the option and click.
Girija said:
1 decade ago
Hi @Ajay,
A, B, C have 2hrs time difference.
In the question they told p machine closed at 11:00 am, that means it worked for only 2 hrs, it doesn't mean that P, Q, are machines have 2hrs time difference.
Could you explain the short cut indeed?
A, B, C have 2hrs time difference.
In the question they told p machine closed at 11:00 am, that means it worked for only 2 hrs, it doesn't mean that P, Q, are machines have 2hrs time difference.
Could you explain the short cut indeed?
Kumar said:
1 decade ago
@Sowjanya Hey friends. Can any one suggest why 60/11 is multiplied with 23/60?
Ans:See 23/60 is the Remaining Work and 60/11 is the Time taken to do Remaining work.
By multiplying both we will get total time=23/11.
Hope you Got it.
Ans:See 23/60 is the Remaining Work and 60/11 is the Time taken to do Remaining work.
By multiplying both we will get total time=23/11.
Hope you Got it.
Kumar said:
1 decade ago
@vachu P is working for 2 hrs it is mentioned indirectly.
In question they told all machines started at 9 am and p closed at 11 am means p's Time is 9-10 1 hour and 10-11 2 hrs Total p's machine Time is 2 Hours Right.
In question they told all machines started at 9 am and p closed at 11 am means p's Time is 9-10 1 hour and 10-11 2 hrs Total p's machine Time is 2 Hours Right.
Sowjanya said:
1 decade ago
Hey friends. Can any one suggest why 60/11 is multiplied with 23/60?
Swapnil said:
8 years ago
Can someone tell me why 1 is subtracted in third step after getting two hours work.
1-37/60 ? Why?
1-37/60 ? Why?
Swapna Vallala said:
8 years ago
The difference between every machine is two hours, so 2hr + 11hr = 13 hrs, ie 1:00 clock. This is an easy method for understanding.
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