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 3 of 10.
Janie said:
5 years ago
The solution is;
10 - 8=2
12 - 10=2
So, two is a common difference.
Then, P is closed at 11:AM.
11:00 + 00:30 = 11:30.
Continued for four good times then you'll get 1:00PM.
10 - 8=2
12 - 10=2
So, two is a common difference.
Then, P is closed at 11:AM.
11:00 + 00:30 = 11:30.
Continued for four good times then you'll get 1:00PM.
Parkavi said:
5 years ago
@All.
The solution is;
P Q R together work for 2 hrs
P + Q + R = 37 *2 = 74,
120-74 = 46.
Remaining 46 works done by Q and R so;
46/22.
23/11 ------ 2 1/11 hours approximately 2 hours.
So, from 11 Am +2 hrs = 1 Pm.
The solution is;
P Q R together work for 2 hrs
P + Q + R = 37 *2 = 74,
120-74 = 46.
Remaining 46 works done by Q and R so;
46/22.
23/11 ------ 2 1/11 hours approximately 2 hours.
So, from 11 Am +2 hrs = 1 Pm.
Vishal R said:
5 years ago
I think we can do like this!
We need to find (Q+R) Work ! Since, We can write it as,
(Q+R ) = (P+Q+R ) - P ---> 1.
Therefore , P+Q+R = (1/8)+(1/10)+(1/12) = 37/120.
All of them Printed for 2 hrs, So (37/160) * 2 = 37/60.
Now find the Individual Work done by P,
P= (1/8), for 2 hrs (1/8)*2 = 1/4.
1--> (Q+R) = (37/60) - (1/4) = 11/30.
Therefore Taking, 30/11 = (approximately 2 hrs).
11 hrs + 2 hrs = 1 PM.
I hope this will be Easy to Understand!
We need to find (Q+R) Work ! Since, We can write it as,
(Q+R ) = (P+Q+R ) - P ---> 1.
Therefore , P+Q+R = (1/8)+(1/10)+(1/12) = 37/120.
All of them Printed for 2 hrs, So (37/160) * 2 = 37/60.
Now find the Individual Work done by P,
P= (1/8), for 2 hrs (1/8)*2 = 1/4.
1--> (Q+R) = (37/60) - (1/4) = 11/30.
Therefore Taking, 30/11 = (approximately 2 hrs).
11 hrs + 2 hrs = 1 PM.
I hope this will be Easy to Understand!
Gayathri said:
5 years ago
Total work needs to be completed = lcm (8,10,12) = 120 work.
Efficiency of P (work completed in 1 hr) = 120/8=15 work.
Similarly for Q=12 work and for R = 10.
Total work done by all the three in 1 hr =15+12+10 =37.
From 9 to 11 am all worked together ie. 37*2 =75 work completed out of 120.
Remaining work =120-75 = 45.
Work completed by Q and R in 1 hr = 10+12 =22.
Time taken to complete 45 work ==> 45/22 ~ 2 hrs.
ie.11 AM + 2 hrs ==> Around 1 PM work will be finished.
Efficiency of P (work completed in 1 hr) = 120/8=15 work.
Similarly for Q=12 work and for R = 10.
Total work done by all the three in 1 hr =15+12+10 =37.
From 9 to 11 am all worked together ie. 37*2 =75 work completed out of 120.
Remaining work =120-75 = 45.
Work completed by Q and R in 1 hr = 10+12 =22.
Time taken to complete 45 work ==> 45/22 ~ 2 hrs.
ie.11 AM + 2 hrs ==> Around 1 PM work will be finished.
Tanuj Upadhyay said:
5 years ago
Work from 9 AM to 11 AM,
=> P+Q+R = (1/8+1/10+1/12) * 2.
=> P+Q+R = 37/60.
After 11 AM only Q & R works, So
=> Q+R = 1/10+1/12.
=> Q+R = 11/60 , this is 1 hour work.
As we know if the total work is done it will be 1.
Now predict the hours,
(37/60)+(11/60)+(11/60) => approx 1.
(2) + (1) + (1) => 4 hours.
From (9+4) AM ->> 1 PM.
=> P+Q+R = (1/8+1/10+1/12) * 2.
=> P+Q+R = 37/60.
After 11 AM only Q & R works, So
=> Q+R = 1/10+1/12.
=> Q+R = 11/60 , this is 1 hour work.
As we know if the total work is done it will be 1.
Now predict the hours,
(37/60)+(11/60)+(11/60) => approx 1.
(2) + (1) + (1) => 4 hours.
From (9+4) AM ->> 1 PM.
(1)
Tanmay chahande said:
5 years ago
See,
P works for 8 hours.
Q works for 10 hours.
R works for 12 hours.
The total time taken by the three machines is 30 hours that is 1 day and 6 hours.
Next condition says that three machines start at 9,00 am and p stops in 2 hours means machines worked for 1 Day and 4 hours now when we calculate 1 day 4 hours from 9.00 am we get clock time 1.00 pm.
P works for 8 hours.
Q works for 10 hours.
R works for 12 hours.
The total time taken by the three machines is 30 hours that is 1 day and 6 hours.
Next condition says that three machines start at 9,00 am and p stops in 2 hours means machines worked for 1 Day and 4 hours now when we calculate 1 day 4 hours from 9.00 am we get clock time 1.00 pm.
(2)
Priyanka said:
5 years ago
As P works for 2hrs that is 9 am to 11am.
Consider for 2hrs
1lakh is done in 8hrs
2hrs..??
(2*100000)/8 = 25000.
Same for Q and R.
(2*100000)/10 = 20000 --->Q.
(2*100000)/12~~16000 --->R.
25000 + 20000 + 16000 = 61000.
In 2 hrs total books are printed are 61000
100000 - 61000 = 39000.
Remaining work is 39000.
Q+R work in 2hrs.
Q+R = 20000 + 16000 = 36000.
Approximately within 2hours Q and R can complete a work.
Consider for 2hrs
1lakh is done in 8hrs
2hrs..??
(2*100000)/8 = 25000.
Same for Q and R.
(2*100000)/10 = 20000 --->Q.
(2*100000)/12~~16000 --->R.
25000 + 20000 + 16000 = 61000.
In 2 hrs total books are printed are 61000
100000 - 61000 = 39000.
Remaining work is 39000.
Q+R work in 2hrs.
Q+R = 20000 + 16000 = 36000.
Approximately within 2hours Q and R can complete a work.
Rohan said:
5 years ago
Why we didn't add the P's work at the end? Please explain.
Shiva said:
6 years ago
We can also do by this method,
Lcm of 8, 10 and 12 is 120.
Suppose total work is 120.
Then, 120/8 = 15.
120/10 = 12.
120/12 = 10.
Now above are respective capacities and we know that work = capacity x time
Hence we have,
15x2+12x+10x = 120.
22x = 90
x = 4 answer.
Lcm of 8, 10 and 12 is 120.
Suppose total work is 120.
Then, 120/8 = 15.
120/10 = 12.
120/12 = 10.
Now above are respective capacities and we know that work = capacity x time
Hence we have,
15x2+12x+10x = 120.
22x = 90
x = 4 answer.
Divya said:
6 years ago
Total work=lcm of 8, 10, 12 = 120.
Work = efficiency * time.
P's efficiency = 120 ÷ 8 = 15 (P's 1hour work).
Q's effi =120 ÷ 10 = 12
R's effi = 120 ÷ 12 = 10.
(P+Q+R)'s together's 2hours work=2 *(15+12+10) = 74 (upto 9 to 11).
Remaining work=120-74 = 46.
(Q+R)'s 2 hours work = 2 * (12+10) = 44 (11 to 1).
Remaining work = 46 - 44 = 2.
Approximately at 1pm work will complete.
Work = efficiency * time.
P's efficiency = 120 ÷ 8 = 15 (P's 1hour work).
Q's effi =120 ÷ 10 = 12
R's effi = 120 ÷ 12 = 10.
(P+Q+R)'s together's 2hours work=2 *(15+12+10) = 74 (upto 9 to 11).
Remaining work=120-74 = 46.
(Q+R)'s 2 hours work = 2 * (12+10) = 44 (11 to 1).
Remaining work = 46 - 44 = 2.
Approximately at 1pm work will complete.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers