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.
PADAMATA PAVAN KUMAR said:
1 year ago
Total unit of work is 240 units.p done per hour 30 units and q done 24 units and r done 20 units per hour.
Now three worked per 2 hr i.e 2(30×24×20)=148 units, remaining=240-148=92 units.
Now p left so only q and r can do in 1 hr (24+20)=44 units .
If they both worked for 2hr.
i.e 44×2=88 units then the total work will finish here 92approx 88,
So, take 2 hr 11 to 2 hr means 1 P.M.
Now three worked per 2 hr i.e 2(30×24×20)=148 units, remaining=240-148=92 units.
Now p left so only q and r can do in 1 hr (24+20)=44 units .
If they both worked for 2hr.
i.e 44×2=88 units then the total work will finish here 92approx 88,
So, take 2 hr 11 to 2 hr means 1 P.M.
(3)
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)
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.
Swedha said:
8 years ago
P=8hours..which implies 2hours=P/4 ie q fourth(0.25) of the work is done by p in 2 hours. Q=10 hours.
Therefore Q's 2 hours work is 0.2. Similarly R's 2 hours work is 0.16
Therefore 2 hours work is 0.25+0.2+0.16=0.616
Remaining work to be done=1-0.616=0.3833
Q+R 1hr work= 1/10+1/12=11/60=0.1833
Next 1 hr work=0.1833
0.1833+0.1833=0.3666.
11+2 hours= 1 pm.
Therefore Q's 2 hours work is 0.2. Similarly R's 2 hours work is 0.16
Therefore 2 hours work is 0.25+0.2+0.16=0.616
Remaining work to be done=1-0.616=0.3833
Q+R 1hr work= 1/10+1/12=11/60=0.1833
Next 1 hr work=0.1833
0.1833+0.1833=0.3666.
11+2 hours= 1 pm.
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)
Nav Raj Bhatta said:
4 years ago
Here,
P take a time to complete the work = 8 hours.
Q take the time to complete the work =10 hours,
R take the time to complete the work=12 hours,
One hour work by PQR=15+10+12 = 37.
Now LCM =120(total unit to complete) (120 unit means 100000).
Now time taken to complete 120 unit = 37*2 (9-11)+22 (11-12)+22(12-13)=120 unit completed till 1 AM.
P take a time to complete the work = 8 hours.
Q take the time to complete the work =10 hours,
R take the time to complete the work=12 hours,
One hour work by PQR=15+10+12 = 37.
Now LCM =120(total unit to complete) (120 unit means 100000).
Now time taken to complete 120 unit = 37*2 (9-11)+22 (11-12)+22(12-13)=120 unit completed till 1 AM.
Akash said:
9 years ago
100000 books
P = 8h.
Q = 10h.
R = 12h.
No of books in 1h:
P = 100000/8 = 12500.
Q = 100000/10 = 10000.
R = 100000/12 = 8333.3.
9am to 11am = 2 hrs
In 2 hrs:
P = 25000.
Q = 20000.
R = 16666.6.
P + Q + R = 61666.6.
LEFT = 100000 - 61666.6 = 38333.4.
After 1h Q + R = 18333.3.
LEFT = 20000.
Again After 1h Q + R = 18333.3.
Approximately at 1pm.
P = 8h.
Q = 10h.
R = 12h.
No of books in 1h:
P = 100000/8 = 12500.
Q = 100000/10 = 10000.
R = 100000/12 = 8333.3.
9am to 11am = 2 hrs
In 2 hrs:
P = 25000.
Q = 20000.
R = 16666.6.
P + Q + R = 61666.6.
LEFT = 100000 - 61666.6 = 38333.4.
After 1h Q + R = 18333.3.
LEFT = 20000.
Again After 1h Q + R = 18333.3.
Approximately at 1pm.
Alok rai said:
1 decade ago
By using concept of percentage
A's 1 day work=100/8%=12.5%
B's 1 day work=100/10%=10%
C's 1 day work=100/12%=8.5%
(A+B+C)'s 1 day work=12.5+10+8.5=31%
(A+B+C)'s 2 day work=31%*2=62%
remaining work =100%-62%=38%
(B+C)'s 1 day work=10.5%+8.5=19%
Therefore
time taken by A and B to complete the remaining work=38/19=2 hr
hence work finished at 1 pm.
A's 1 day work=100/8%=12.5%
B's 1 day work=100/10%=10%
C's 1 day work=100/12%=8.5%
(A+B+C)'s 1 day work=12.5+10+8.5=31%
(A+B+C)'s 2 day work=31%*2=62%
remaining work =100%-62%=38%
(B+C)'s 1 day work=10.5%+8.5=19%
Therefore
time taken by A and B to complete the remaining work=38/19=2 hr
hence work finished at 1 pm.
Aaren said:
1 year ago
@All.
According to me, the Time taken for P, Q, R machines together to print everything will be 120/37 ~3.5 hours or about 12:30 pm.
So, if one machine stops working in between then obviously it will take more time than 12:30 and there was only one option satisfying this condition.
Anyone, please clarify this to me clearly.
According to me, the Time taken for P, Q, R machines together to print everything will be 120/37 ~3.5 hours or about 12:30 pm.
So, if one machine stops working in between then obviously it will take more time than 12:30 and there was only one option satisfying this condition.
Anyone, please clarify this to me clearly.
(9)
Revathi Yadavalli said:
9 years ago
Hi,
I did this solution as follows any one tell to me its right or wrong.
P = 1L - 8Hrs.
Q = 1L - 10Hrs.
R = 1L = 12Hrs.
The time difference between P, Q, R is 2hrs only.
So,
P Work starts 9AM And Finished it 11AM.
Q Work starts 9AM And Finished it 13PM (11+2).
R Work starts 9AM And Finished it 15PM (13+2).
I did this solution as follows any one tell to me its right or wrong.
P = 1L - 8Hrs.
Q = 1L - 10Hrs.
R = 1L = 12Hrs.
The time difference between P, Q, R is 2hrs only.
So,
P Work starts 9AM And Finished it 11AM.
Q Work starts 9AM And Finished it 13PM (11+2).
R Work starts 9AM And Finished it 15PM (13+2).
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