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 7 of 10.
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.
Ramya said:
7 years ago
How we take P is working for 2 hour, it is not mentioned here?
Akil Prakash said:
7 years ago
Well said @Sameer. Thanks.
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
Pranot said:
6 years ago
Why we are subtracting 1-37/60? please explain.
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.
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.
Rohan said:
5 years ago
Why we didn't add the P's work at the end? Please explain.
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.
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)
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