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:
96 comments Page 10 of 10.
Aaren said:
2 years 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)
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)
Preetithapa said:
10 months ago
p-8hr , Q -10hr R - 12 hr.
Total work (LCM) - 120 unit.
Efficiency of P, Q, R - 15, 12, 10 .
For 2hr - 2(15+12+10) = 74 unit.
The remaining work- 46 units.
The time taken by (Q+R) =2.09 hr ~2hr.
9:00am + 2hr = 11 am.
11am + 2hr = 1 pm.
Total work (LCM) - 120 unit.
Efficiency of P, Q, R - 15, 12, 10 .
For 2hr - 2(15+12+10) = 74 unit.
The remaining work- 46 units.
The time taken by (Q+R) =2.09 hr ~2hr.
9:00am + 2hr = 11 am.
11am + 2hr = 1 pm.
(20)
Barshan Roy said:
8 months ago
Well explained. Thanks all.
(2)
Harini Murali said:
4 months ago
P - 1,00,000 = 8H.
Q - 1,00,000 = 10H.
R - 1,00,000 = 12H.
P, Q, R start at 9.00AM,
P = 11.00AM finished,
R - P = 2H.
Total 2 hrs difference,
11.00AM + 2 = 1:00 PM.
Then Ans : 1.00pm.
Q - 1,00,000 = 10H.
R - 1,00,000 = 12H.
P, Q, R start at 9.00AM,
P = 11.00AM finished,
R - P = 2H.
Total 2 hrs difference,
11.00AM + 2 = 1:00 PM.
Then Ans : 1.00pm.
(8)
Saurabh said:
4 weeks ago
Very easy approach.
Work to do (W) -> print 1 lakh books.
Machine P can do that work W in 8 hours.
Machine Q can do that work W in 10 hours.
Machine R can do that work W in 12 hours.
All machines started at 9 AM means all Machines P,Q and R are working together till 11 AM, meaning 2 hours together
So we write W/8 +W/10 +W/12, which together gives us per per-hour work (print) of each machine
->they did that together for two hours, so we multiply it by 2
2(W/8 + W/10 + W/12).
P is switched off at 11 AM means now remaining to machines Q and R will do the remaining work.
(W/10 + W/12)
But for how long these remaining machines are doing this remaining work, let's say x hours.
x(W/10 + W/12).
So total.
2(W/8 +W/10 +W/12) +x (W/10 +W/12) = W = total work.
solving for x , we get;
x ~= 2 hours.
Machines started from 9Am to 9Am + x time. So we get 1 AM as an Answer.
Work to do (W) -> print 1 lakh books.
Machine P can do that work W in 8 hours.
Machine Q can do that work W in 10 hours.
Machine R can do that work W in 12 hours.
All machines started at 9 AM means all Machines P,Q and R are working together till 11 AM, meaning 2 hours together
So we write W/8 +W/10 +W/12, which together gives us per per-hour work (print) of each machine
->they did that together for two hours, so we multiply it by 2
2(W/8 + W/10 + W/12).
P is switched off at 11 AM means now remaining to machines Q and R will do the remaining work.
(W/10 + W/12)
But for how long these remaining machines are doing this remaining work, let's say x hours.
x(W/10 + W/12).
So total.
2(W/8 +W/10 +W/12) +x (W/10 +W/12) = W = total work.
solving for x , we get;
x ~= 2 hours.
Machines started from 9Am to 9Am + x time. So we get 1 AM as an Answer.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers