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.
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)
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)
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)
Atul said:
3 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)
Pranot said:
6 years ago
Why we are subtracting 1-37/60? please explain.
Parkavi said:
5 years ago
@All.
The solution is;
P Q R together work for 2 hrs
P + Q + R = 37 *2 = 74,
120-74 = 46.
Remaining 46 works done by Q and R so;
46/22.
23/11 ------ 2 1/11 hours approximately 2 hours.
So, from 11 Am +2 hrs = 1 Pm.
The solution is;
P Q R together work for 2 hrs
P + Q + R = 37 *2 = 74,
120-74 = 46.
Remaining 46 works done by Q and R so;
46/22.
23/11 ------ 2 1/11 hours approximately 2 hours.
So, from 11 Am +2 hrs = 1 Pm.
Vishal R said:
5 years ago
I think we can do like this!
We need to find (Q+R) Work ! Since, We can write it as,
(Q+R ) = (P+Q+R ) - P ---> 1.
Therefore , P+Q+R = (1/8)+(1/10)+(1/12) = 37/120.
All of them Printed for 2 hrs, So (37/160) * 2 = 37/60.
Now find the Individual Work done by P,
P= (1/8), for 2 hrs (1/8)*2 = 1/4.
1--> (Q+R) = (37/60) - (1/4) = 11/30.
Therefore Taking, 30/11 = (approximately 2 hrs).
11 hrs + 2 hrs = 1 PM.
I hope this will be Easy to Understand!
We need to find (Q+R) Work ! Since, We can write it as,
(Q+R ) = (P+Q+R ) - P ---> 1.
Therefore , P+Q+R = (1/8)+(1/10)+(1/12) = 37/120.
All of them Printed for 2 hrs, So (37/160) * 2 = 37/60.
Now find the Individual Work done by P,
P= (1/8), for 2 hrs (1/8)*2 = 1/4.
1--> (Q+R) = (37/60) - (1/4) = 11/30.
Therefore Taking, 30/11 = (approximately 2 hrs).
11 hrs + 2 hrs = 1 PM.
I hope this will be Easy to Understand!
Gayathri said:
5 years ago
Total work needs to be completed = lcm (8,10,12) = 120 work.
Efficiency of P (work completed in 1 hr) = 120/8=15 work.
Similarly for Q=12 work and for R = 10.
Total work done by all the three in 1 hr =15+12+10 =37.
From 9 to 11 am all worked together ie. 37*2 =75 work completed out of 120.
Remaining work =120-75 = 45.
Work completed by Q and R in 1 hr = 10+12 =22.
Time taken to complete 45 work ==> 45/22 ~ 2 hrs.
ie.11 AM + 2 hrs ==> Around 1 PM work will be finished.
Efficiency of P (work completed in 1 hr) = 120/8=15 work.
Similarly for Q=12 work and for R = 10.
Total work done by all the three in 1 hr =15+12+10 =37.
From 9 to 11 am all worked together ie. 37*2 =75 work completed out of 120.
Remaining work =120-75 = 45.
Work completed by Q and R in 1 hr = 10+12 =22.
Time taken to complete 45 work ==> 45/22 ~ 2 hrs.
ie.11 AM + 2 hrs ==> Around 1 PM work will be finished.
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.
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.
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