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 4 of 10.
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?
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.
Devi said:
8 years ago
How to calculate 2 hours from 23/11 hours? Please help me, I'm in confusion.
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).
BUVANA said:
9 years ago
Nice explanation @Sukanya.
Kuldeep kumar said:
9 years ago
P do work in one hour = 100000/8 = 12500print.
Similarly;
q=10000print in one hour
R=8333.3print in one hour
So P and Q and R together work
continous = 2 * (12500+10000+8333.3)=61666.6 ------- (i) Print Page In 11am.
After 11 am left
Left print 100000-61666.6 = 38333.4.
And now P is closed and Q or R.
The contuinous work so next TWO HOUR PRINT pages By P And Q
= 2 * (10000+8333.3) =36666.6-----(ii)
Now All print page eq(i) + eq(ii) = 98333.2
So, approximately 11am + 2am = 1am approx ANS.
Similarly;
q=10000print in one hour
R=8333.3print in one hour
So P and Q and R together work
continous = 2 * (12500+10000+8333.3)=61666.6 ------- (i) Print Page In 11am.
After 11 am left
Left print 100000-61666.6 = 38333.4.
And now P is closed and Q or R.
The contuinous work so next TWO HOUR PRINT pages By P And Q
= 2 * (10000+8333.3) =36666.6-----(ii)
Now All print page eq(i) + eq(ii) = 98333.2
So, approximately 11am + 2am = 1am approx ANS.
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.
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