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 1 of 10.
Sowjanya said:
1 decade ago
Hey friends. Can any one suggest why 60/11 is multiplied with 23/60?
Pandu said:
1 decade ago
This problem code is length. Please any shortcut of this problem.
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
Sameer said:
1 decade ago
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
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
(1)
Vachu said:
1 decade ago
Why p is working for two hrs its ont mentioned?
Shashank said:
1 decade ago
Easy Solution
let total time to print the book be x
therefore
x-2/8 + x/10 + x/12= 1
Solve for x we get approx 4
so time will be 9+4=1 pm.
let total time to print the book be x
therefore
x-2/8 + x/10 + x/12= 1
Solve for x we get approx 4
so time will be 9+4=1 pm.
Gayu said:
1 decade ago
Hey is above told methods are applicable? to this type of problems with a small change.
Naveen kumar said:
1 decade ago
Hi friends... In this problem it is having some confusion in the last step....i will explain that step in a easy way....
The work completed by q and r after closing of p machine is
23/60....
but we don't know the time...
we have to calculate it...
(q+r)'s 1 hour work = 11/60.
we can represent the above relation like this....
11/60 (portion of work)-------> 1 hour (time)
23/60 (portion of work) ------> ....? (time)
By cross multiplying the above terms we will get.
11/60 * 60/23 = 23/11
that is approximately equals to 2 ....
q and r machines took 2 hours to complete the remaining work....
i.e.,
11+2 = 1 p.m
the total 1 lakh books will be printed by 1 p.m
The work completed by q and r after closing of p machine is
23/60....
but we don't know the time...
we have to calculate it...
(q+r)'s 1 hour work = 11/60.
we can represent the above relation like this....
11/60 (portion of work)-------> 1 hour (time)
23/60 (portion of work) ------> ....? (time)
By cross multiplying the above terms we will get.
11/60 * 60/23 = 23/11
that is approximately equals to 2 ....
q and r machines took 2 hours to complete the remaining work....
i.e.,
11+2 = 1 p.m
the total 1 lakh books will be printed by 1 p.m
Syed said:
1 decade ago
Can some one tell me why 1-37/60 ?
Div said:
1 decade ago
Since machine p stops after 37 units of work is completed from 60 units of work, still (60-37=23) 23units of work is remaining. hence, 1-(37/60)= 23/60
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