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 4 of 10.
Pranot said:
6 years ago
Why we are subtracting 1-37/60? please explain.
Velmurugan R said:
7 years ago
P's time taken- 8 hrs
Q's taken- 10 hrs
R's taken- 12 hrs
Total work to be completed= 120 (LCM of 8,10,12)
Now,
P's one hr work= 120/8 = 15,
Q's work/hr= 120/10= 12,
R's work/ hr= 120/12= 10.
Here,
(P+Q+R)work/hr= (15+12+10)= 37.
After 11am P stops, therefore,
1st 2hrs work= (37*2)= 74.
Remaining work after 2 hrs,
= (120-74)= 46.
46 work need to complete after 2 hrs with Q and R. Now Q & R's work/hr
= (12+10)= 22 wrk/hr.
So, Remaining 46 work to be completed in = (46/22)= 2 (approx.)
It takes 2 hrs after 11am.
So, the Answer is 1pm
Q's taken- 10 hrs
R's taken- 12 hrs
Total work to be completed= 120 (LCM of 8,10,12)
Now,
P's one hr work= 120/8 = 15,
Q's work/hr= 120/10= 12,
R's work/ hr= 120/12= 10.
Here,
(P+Q+R)work/hr= (15+12+10)= 37.
After 11am P stops, therefore,
1st 2hrs work= (37*2)= 74.
Remaining work after 2 hrs,
= (120-74)= 46.
46 work need to complete after 2 hrs with Q and R. Now Q & R's work/hr
= (12+10)= 22 wrk/hr.
So, Remaining 46 work to be completed in = (46/22)= 2 (approx.)
It takes 2 hrs after 11am.
So, the Answer is 1pm
Akil Prakash said:
7 years ago
Well said @Sameer. Thanks.
Ramya said:
7 years ago
How we take P is working for 2 hour, it is not mentioned here?
Saeem momin said:
7 years ago
Simplest calculation: quite long because only logic is used in this solution.
One lakhs books is to be printed okay and each machine prints the same number of books but on different hours so iF machine.
A takes 8 hours to print one lakh books so.
No of books printed in an hour by A = one lakh/8 =12500 books is printed in an hour.
And A worked for two hours so it will print 25000 books.
And now machine Q will take 12 hours to print one lakhs books.
No of books printed in an hour by q = one lakh/ 12 = approx 8333 books for one hour.
For two hours it ill print 16666 approx books.
And machine are will take 10 hours to print one lakh = one lakh/ 10 = 10000 books for an hour.
So for two hours, it will print 20000 books.
So till 11 am the number of books printed is 25000+16666+20000= approx 61666 books.
Remaining books to be printed is 100000-61666.
Add remaining books from other machines from q and are and count no of extra hours added to make the count one lakh.
One lakhs books is to be printed okay and each machine prints the same number of books but on different hours so iF machine.
A takes 8 hours to print one lakh books so.
No of books printed in an hour by A = one lakh/8 =12500 books is printed in an hour.
And A worked for two hours so it will print 25000 books.
And now machine Q will take 12 hours to print one lakhs books.
No of books printed in an hour by q = one lakh/ 12 = approx 8333 books for one hour.
For two hours it ill print 16666 approx books.
And machine are will take 10 hours to print one lakh = one lakh/ 10 = 10000 books for an hour.
So for two hours, it will print 20000 books.
So till 11 am the number of books printed is 25000+16666+20000= approx 61666 books.
Remaining books to be printed is 100000-61666.
Add remaining books from other machines from q and are and count no of extra hours added to make the count one lakh.
Shree said:
7 years ago
I got it with the help of given explanation. Thanks all.
Swapnil said:
7 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.
Barun kumar mahalik said:
8 years ago
8+3=11,
10+3=13,
12+3=15,
11+13+15=39/3=13,
13 is called 1pm.
10+3=13,
12+3=15,
11+13+15=39/3=13,
13 is called 1pm.
(1)
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.
Swapnil said:
8 years ago
Can someone tell me why 1 is subtracted in third step after getting two hours work.
1-37/60 ? Why?
1-37/60 ? Why?
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