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 9 of 10.
@bhi said:
10 years ago
Reason for 37/120*2 = 37/60?
Divya said:
10 years ago
How do I get this answer 2*1/8 + (1/10) * x + (1/12) x = 1?
x = 4.09.
x = 4.09.
Balu said:
10 years ago
Hello guys, easy solution:
X-2/8 + X/10 + X/12 = 1 (lik A+B+C's 1 Day Work).
By solving we get X = 4.
So, Machines are started at 9.
= 9+4 = 13 (i.e, 1'O clock).
X-2/8 + X/10 + X/12 = 1 (lik A+B+C's 1 Day Work).
By solving we get X = 4.
So, Machines are started at 9.
= 9+4 = 13 (i.e, 1'O clock).
Sparton said:
1 decade ago
Nice methods explains above thank you friends.
Ashna said:
1 decade ago
P in 1 hr-----1/8.
Q in 1 hr-----1/10.
R in 1 hr-----1/12.
Therefore 2/8+(x+2)/10+(x+2)/12 = 1.
On solving x=23/11=2 hrs. (approx).
Therefore, 11 A.M.+2hr = 1 P.M.
Q in 1 hr-----1/10.
R in 1 hr-----1/12.
Therefore 2/8+(x+2)/10+(x+2)/12 = 1.
On solving x=23/11=2 hrs. (approx).
Therefore, 11 A.M.+2hr = 1 P.M.
Sojib said:
9 years ago
Can anyone give an easy and simple solution?
Basant Kumar said:
1 decade ago
P takes = 8 hrs.
Q takes = 10 hrs.
R takes = 12 hrs.
We assume total work as the LCM of 8, 10, 12 = 120.
P completes 15 unit/hours.
Q = 12 unit/hrs.
R = 10 unit/hrs.
P+Q+R together = 37 unit/hours.
They continue to work for 2 hours i.e. 37x2 = 74 unit is completed.
Remaining work = 120-74 = 46 units.
Remaining work is done by Q and R,
So, P+Q = 22 unit/hours.
They will take 2 hours more to complete remaining work.
22x2 = 46 units.
Work will complete in total 4 hours.
So, at 1:00 PM.
Q takes = 10 hrs.
R takes = 12 hrs.
We assume total work as the LCM of 8, 10, 12 = 120.
P completes 15 unit/hours.
Q = 12 unit/hrs.
R = 10 unit/hrs.
P+Q+R together = 37 unit/hours.
They continue to work for 2 hours i.e. 37x2 = 74 unit is completed.
Remaining work = 120-74 = 46 units.
Remaining work is done by Q and R,
So, P+Q = 22 unit/hours.
They will take 2 hours more to complete remaining work.
22x2 = 46 units.
Work will complete in total 4 hours.
So, at 1:00 PM.
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.
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