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 6 of 10.
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.
BUVANA said:
9 years ago
Nice explanation @Sukanya.
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).
Devi said:
8 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.
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?
Swedha said:
8 years ago
P=8hours..which implies 2hours=P/4 ie q fourth(0.25) of the work is done by p in 2 hours. Q=10 hours.
Therefore Q's 2 hours work is 0.2. Similarly R's 2 hours work is 0.16
Therefore 2 hours work is 0.25+0.2+0.16=0.616
Remaining work to be done=1-0.616=0.3833
Q+R 1hr work= 1/10+1/12=11/60=0.1833
Next 1 hr work=0.1833
0.1833+0.1833=0.3666.
11+2 hours= 1 pm.
Therefore Q's 2 hours work is 0.2. Similarly R's 2 hours work is 0.16
Therefore 2 hours work is 0.25+0.2+0.16=0.616
Remaining work to be done=1-0.616=0.3833
Q+R 1hr work= 1/10+1/12=11/60=0.1833
Next 1 hr work=0.1833
0.1833+0.1833=0.3666.
11+2 hours= 1 pm.
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)
Swapnil said:
7 years ago
@ALL.
See 37/120 is a work done of PQR in 1hr
Now p is close after 2 hrs it means PQR combine work for 2 hrs.
So work done by PQR in 2 hrs,
2* 37/120 = 37/60.
Remaining work 1-37/60 = 23/60,
23/60 work is done by only Q and R after closing of P,
Q and R 1 hr work ,
1/10 + 1/12 = 11/60.
So whole work completed by Q and R in 60/11 hr,
But in problem Q and R combine do only 23/60,
That's why 60/11 * 23/60= 23/11 = ~2 hr.
Whole work completed 11+ 2 =13= 1 pm.
See 37/120 is a work done of PQR in 1hr
Now p is close after 2 hrs it means PQR combine work for 2 hrs.
So work done by PQR in 2 hrs,
2* 37/120 = 37/60.
Remaining work 1-37/60 = 23/60,
23/60 work is done by only Q and R after closing of P,
Q and R 1 hr work ,
1/10 + 1/12 = 11/60.
So whole work completed by Q and R in 60/11 hr,
But in problem Q and R combine do only 23/60,
That's why 60/11 * 23/60= 23/11 = ~2 hr.
Whole work completed 11+ 2 =13= 1 pm.
Shree said:
7 years ago
I got it with the help of given explanation. Thanks all.
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