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 3 of 10.
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)
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)
Saurabh said:
2 months 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.
(1)
Atul said:
4 years ago
By basic formula we know that.
E * T = W (where E = Efficiency, T = time, W = work).
so let machine P's E = 1.
then e*t = w.
1 * 8 = 8.
Total work = 8,
now all machines run for 2 hour.
So, 2h work.
(1 + 4/5 +2/3) = efficiency of all machine together = 37/15 ( 8/8, 8/10, 8/12), here I calculate the efficiency of every machine.
37/15 * 2 = 74/15.
remaining work = total work - work done.
= 8- 74/15 = 46/15.
Now P left then remaining efficiency = 4/5 + 2/3 = 22/15.
now,
22/15 * t = 46/15.
t = 46/15.
t = 2(approx).
So, total time = 2+2 = 4h.
9am +4 h = 1pm.
E * T = W (where E = Efficiency, T = time, W = work).
so let machine P's E = 1.
then e*t = w.
1 * 8 = 8.
Total work = 8,
now all machines run for 2 hour.
So, 2h work.
(1 + 4/5 +2/3) = efficiency of all machine together = 37/15 ( 8/8, 8/10, 8/12), here I calculate the efficiency of every machine.
37/15 * 2 = 74/15.
remaining work = total work - work done.
= 8- 74/15 = 46/15.
Now P left then remaining efficiency = 4/5 + 2/3 = 22/15.
now,
22/15 * t = 46/15.
t = 46/15.
t = 2(approx).
So, total time = 2+2 = 4h.
9am +4 h = 1pm.
(1)
Sameer said:
1 decade ago
P 1hrs work 1/8
Q 1hrs work 1/10
R 1hrs work 1/12
p worked for 2 hrs so 2*1/8
suppose Q and r worked for 'x' hrs
then,
2*1/8+(1/10)*x+(1/12)x = 1
x=4.09
ans 9+4.09 = 1pm
Q 1hrs work 1/10
R 1hrs work 1/12
p worked for 2 hrs so 2*1/8
suppose Q and r worked for 'x' hrs
then,
2*1/8+(1/10)*x+(1/12)x = 1
x=4.09
ans 9+4.09 = 1pm
(1)
Sudharshan said:
9 years ago
I didn't understand @Sukanya.
BUVANA said:
9 years ago
Nice explanation @Sukanya.
Kranthi said:
9 years ago
P can work 2 hours 2/8 = 1/4.
We don't know how much Q and R work so let be think as = x.
1/4 + x/10 + x/12 =1.
LCM 60.
15+6x+5x=60,
15+11x=60,
11x=45,
X=4.~.
Work started at 9 so add 4 hours = 9+4 = 13 (1P.M).
We don't know how much Q and R work so let be think as = x.
1/4 + x/10 + x/12 =1.
LCM 60.
15+6x+5x=60,
15+11x=60,
11x=45,
X=4.~.
Work started at 9 so add 4 hours = 9+4 = 13 (1P.M).
Devi said:
9 years ago
How to calculate 2 hours from 23/11 hours? Please help me, I'm in confusion.
Swapna Vallala said:
8 years ago
The difference between every machine is two hours, so 2hr + 11hr = 13 hrs, ie 1:00 clock. This is an easy method for understanding.
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