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 9 of 10.
Devi said:
8 years ago
How to calculate 2 hours from 23/11 hours? Please help me, I'm in confusion.
Kranthi said:
8 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.
Sojib said:
9 years ago
Can anyone give an easy and simple solution?
Sudharshan said:
9 years ago
I didn't understand @Sukanya.
Kumar said:
1 decade ago
@sneha Its just taking Lcm for 1/8+1/10+1/12 you il get 37/120.
Lcm for 8, 10, 12 is 120.
8 goes 15 times in 120 and 10 goes 12 times in 120 and 12 goes 10 times in 120.
By adding 15+10+12=37 you will get.
Hope you got it.
Lcm for 8, 10, 12 is 120.
8 goes 15 times in 120 and 10 goes 12 times in 120 and 12 goes 10 times in 120.
By adding 15+10+12=37 you will get.
Hope you got it.
Akash said:
9 years ago
100000 books
P = 8h.
Q = 10h.
R = 12h.
No of books in 1h:
P = 100000/8 = 12500.
Q = 100000/10 = 10000.
R = 100000/12 = 8333.3.
9am to 11am = 2 hrs
In 2 hrs:
P = 25000.
Q = 20000.
R = 16666.6.
P + Q + R = 61666.6.
LEFT = 100000 - 61666.6 = 38333.4.
After 1h Q + R = 18333.3.
LEFT = 20000.
Again After 1h Q + R = 18333.3.
Approximately at 1pm.
P = 8h.
Q = 10h.
R = 12h.
No of books in 1h:
P = 100000/8 = 12500.
Q = 100000/10 = 10000.
R = 100000/12 = 8333.3.
9am to 11am = 2 hrs
In 2 hrs:
P = 25000.
Q = 20000.
R = 16666.6.
P + Q + R = 61666.6.
LEFT = 100000 - 61666.6 = 38333.4.
After 1h Q + R = 18333.3.
LEFT = 20000.
Again After 1h Q + R = 18333.3.
Approximately at 1pm.
Gautham Raj said:
9 years ago
It's very clear now thank you all for explaining this.
Revathi Yadavalli said:
9 years ago
Hi,
I did this solution as follows any one tell to me its right or wrong.
P = 1L - 8Hrs.
Q = 1L - 10Hrs.
R = 1L = 12Hrs.
The time difference between P, Q, R is 2hrs only.
So,
P Work starts 9AM And Finished it 11AM.
Q Work starts 9AM And Finished it 13PM (11+2).
R Work starts 9AM And Finished it 15PM (13+2).
I did this solution as follows any one tell to me its right or wrong.
P = 1L - 8Hrs.
Q = 1L - 10Hrs.
R = 1L = 12Hrs.
The time difference between P, Q, R is 2hrs only.
So,
P Work starts 9AM And Finished it 11AM.
Q Work starts 9AM And Finished it 13PM (11+2).
R Work starts 9AM And Finished it 15PM (13+2).
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