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 2 of 10.
Dhinesh said:
1 year ago
P = 1/8 the amount of work in one day.
Q = 1/10 amount of work in one day.
R = 1/12 amount of work in one day.
All machines start at 9.00 AM.
Machine P stopped at 11.00 AM so it worked 2hrs,
11.00AM - 9.00AM = 2hrs.
P's work in 2hrs = 2(1/8) = 1/4.
Remaining work = 1 - (1/4) = 3/4 pending.
Q+R 's work in one day=(1/10)+(1/12)=11/60
to complete 3/4 of the work, Q and R need 'x' Days.
x(11/60) = 3/4
x = (3/4) * (60/11),
x = 45/11,
x = 4.99 (approx. 5hrs)
5 hours from 9AM is 1.00 PM
Q = 1/10 amount of work in one day.
R = 1/12 amount of work in one day.
All machines start at 9.00 AM.
Machine P stopped at 11.00 AM so it worked 2hrs,
11.00AM - 9.00AM = 2hrs.
P's work in 2hrs = 2(1/8) = 1/4.
Remaining work = 1 - (1/4) = 3/4 pending.
Q+R 's work in one day=(1/10)+(1/12)=11/60
to complete 3/4 of the work, Q and R need 'x' Days.
x(11/60) = 3/4
x = (3/4) * (60/11),
x = 45/11,
x = 4.99 (approx. 5hrs)
5 hours from 9AM is 1.00 PM
(41)
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.
Joel said:
4 years ago
Take lcm of 8, 10'12.
Lcm = 120 units book to be printed.
P = 120/8 = 15 units/ hour.
Q = 120/10 = 12 units per hour.
R = 120/12 = 10 units per hour.
Total units per hour=15+12+10=37 units per hour.
P+q+r work together for two hour=37*2=74 units for two hours.
Remaining work=120-72=46 units.
P and R one hour efficiency=12+10=22 units per hour.
They need how much time to finish 46 units?
46/22 = 2.09 hours.
After 11 am they need 2 hours means 1 pm approximately.
Lcm = 120 units book to be printed.
P = 120/8 = 15 units/ hour.
Q = 120/10 = 12 units per hour.
R = 120/12 = 10 units per hour.
Total units per hour=15+12+10=37 units per hour.
P+q+r work together for two hour=37*2=74 units for two hours.
Remaining work=120-72=46 units.
P and R one hour efficiency=12+10=22 units per hour.
They need how much time to finish 46 units?
46/22 = 2.09 hours.
After 11 am they need 2 hours means 1 pm approximately.
(8)
Swapnil said:
8 years ago
@ALL.
See 37/120 is a work done of PQR in 1hr
Now p is close after 2 hrs it means PQR combine work for 2 hrs.
So work done by PQR in 2 hrs,
2* 37/120 = 37/60.
Remaining work 1-37/60 = 23/60,
23/60 work is done by only Q and R after closing of P,
Q and R 1 hr work ,
1/10 + 1/12 = 11/60.
So whole work completed by Q and R in 60/11 hr,
But in problem Q and R combine do only 23/60,
That's why 60/11 * 23/60= 23/11 = ~2 hr.
Whole work completed 11+ 2 =13= 1 pm.
See 37/120 is a work done of PQR in 1hr
Now p is close after 2 hrs it means PQR combine work for 2 hrs.
So work done by PQR in 2 hrs,
2* 37/120 = 37/60.
Remaining work 1-37/60 = 23/60,
23/60 work is done by only Q and R after closing of P,
Q and R 1 hr work ,
1/10 + 1/12 = 11/60.
So whole work completed by Q and R in 60/11 hr,
But in problem Q and R combine do only 23/60,
That's why 60/11 * 23/60= 23/11 = ~2 hr.
Whole work completed 11+ 2 =13= 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!
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.
Ankit Jha said:
1 decade ago
I did it other way around.
2*(P+Q+R)'s 1 hour work + (Q+R)'s 1 hour work*X = 1.
37/60+(1/10+1/12)*x = 1.
11/60*x = 23/60.
x = 23/11 which is approximately equal to 2.
Hence Total time taken would be the initial two hours where P also contributed and the rest 23/11 i.e. 2 hours where only Q and are contributed.
Therefore, Total time will be 2+2= 4 Hours.
9:00 AM + 4 hours will be 1:00 PM.
Corrections are most welcome.
2*(P+Q+R)'s 1 hour work + (Q+R)'s 1 hour work*X = 1.
37/60+(1/10+1/12)*x = 1.
11/60*x = 23/60.
x = 23/11 which is approximately equal to 2.
Hence Total time taken would be the initial two hours where P also contributed and the rest 23/11 i.e. 2 hours where only Q and are contributed.
Therefore, Total time will be 2+2= 4 Hours.
9:00 AM + 4 hours will be 1:00 PM.
Corrections are most welcome.
Parthiban said:
5 years ago
8,10,12 for this lcm 120
Assume 120 books print
Machines printing per hour
P 120/8 = 15
Q 120/10=12
R 120/12=10.
Per hour 3 machine together print books 37
Start 9 am 11 pm machine p stop the work.
2 hours all machine worked so 2 *37=74.
120-74=46 machine Q R together print in one hour 10+12=22.
So 46/22 =2.02 so 2 hours required to print remains books
After 11 am need 2 hours need so answer 1 pm.
Assume 120 books print
Machines printing per hour
P 120/8 = 15
Q 120/10=12
R 120/12=10.
Per hour 3 machine together print books 37
Start 9 am 11 pm machine p stop the work.
2 hours all machine worked so 2 *37=74.
120-74=46 machine Q R together print in one hour 10+12=22.
So 46/22 =2.02 so 2 hours required to print remains books
After 11 am need 2 hours need so answer 1 pm.
(2)
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.
Dharmendra pandian S said:
3 years ago
P= 1 lakh = for 1 hr 12500.
Q= 1 lakh = for 1 hr 10000.
R= 1 lakh = for 1 hr 8333.
The three of them did for 9:00 am to 11:00 am so the job done is 61,666 books printed and then;
The balance they are 100000-61666 = 38,334.
So, take q +r = 18333 and try with each multiple which is near to that 38,334
18333×2 = 36,666.
So they take 2 hrs add with 11:00 then;
Answer will be 1:00 pm.
Q= 1 lakh = for 1 hr 10000.
R= 1 lakh = for 1 hr 8333.
The three of them did for 9:00 am to 11:00 am so the job done is 61,666 books printed and then;
The balance they are 100000-61666 = 38,334.
So, take q +r = 18333 and try with each multiple which is near to that 38,334
18333×2 = 36,666.
So they take 2 hrs add with 11:00 then;
Answer will be 1:00 pm.
(21)
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers