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 1 of 10.
Harini Murali said:
3 weeks ago
P - 1,00,000 = 8H.
Q - 1,00,000 = 10H.
R - 1,00,000 = 12H.
P, Q, R start at 9.00AM,
P = 11.00AM finished,
R - P = 2H.
Total 2 hrs difference,
11.00AM + 2 = 1:00 PM.
Then Ans : 1.00pm.
Q - 1,00,000 = 10H.
R - 1,00,000 = 12H.
P, Q, R start at 9.00AM,
P = 11.00AM finished,
R - P = 2H.
Total 2 hrs difference,
11.00AM + 2 = 1:00 PM.
Then Ans : 1.00pm.
(3)
Barshan Roy said:
5 months ago
Well explained. Thanks all.
(1)
Preetithapa said:
6 months ago
p-8hr , Q -10hr R - 12 hr.
Total work (LCM) - 120 unit.
Efficiency of P, Q, R - 15, 12, 10 .
For 2hr - 2(15+12+10) = 74 unit.
The remaining work- 46 units.
The time taken by (Q+R) =2.09 hr ~2hr.
9:00am + 2hr = 11 am.
11am + 2hr = 1 pm.
Total work (LCM) - 120 unit.
Efficiency of P, Q, R - 15, 12, 10 .
For 2hr - 2(15+12+10) = 74 unit.
The remaining work- 46 units.
The time taken by (Q+R) =2.09 hr ~2hr.
9:00am + 2hr = 11 am.
11am + 2hr = 1 pm.
(14)
Dhinesh said:
1 year ago
P = 1/8 the amount of work in one day.
Q = 1/10 amount of work in one day.
R = 1/12 amount of work in one day.
All machines start at 9.00 AM.
Machine P stopped at 11.00 AM so it worked 2hrs,
11.00AM - 9.00AM = 2hrs.
P's work in 2hrs = 2(1/8) = 1/4.
Remaining work = 1 - (1/4) = 3/4 pending.
Q+R 's work in one day=(1/10)+(1/12)=11/60
to complete 3/4 of the work, Q and R need 'x' Days.
x(11/60) = 3/4
x = (3/4) * (60/11),
x = 45/11,
x = 4.99 (approx. 5hrs)
5 hours from 9AM is 1.00 PM
Q = 1/10 amount of work in one day.
R = 1/12 amount of work in one day.
All machines start at 9.00 AM.
Machine P stopped at 11.00 AM so it worked 2hrs,
11.00AM - 9.00AM = 2hrs.
P's work in 2hrs = 2(1/8) = 1/4.
Remaining work = 1 - (1/4) = 3/4 pending.
Q+R 's work in one day=(1/10)+(1/12)=11/60
to complete 3/4 of the work, Q and R need 'x' Days.
x(11/60) = 3/4
x = (3/4) * (60/11),
x = 45/11,
x = 4.99 (approx. 5hrs)
5 hours from 9AM is 1.00 PM
(39)
Aaren said:
1 year ago
@All.
According to me, the Time taken for P, Q, R machines together to print everything will be 120/37 ~3.5 hours or about 12:30 pm.
So, if one machine stops working in between then obviously it will take more time than 12:30 and there was only one option satisfying this condition.
Anyone, please clarify this to me clearly.
According to me, the Time taken for P, Q, R machines together to print everything will be 120/37 ~3.5 hours or about 12:30 pm.
So, if one machine stops working in between then obviously it will take more time than 12:30 and there was only one option satisfying this condition.
Anyone, please clarify this to me clearly.
(8)
Keval shah said:
1 year ago
Thanks for the explanation @Sai Vinitha.
(2)
PADAMATA PAVAN KUMAR said:
1 year ago
Total unit of work is 240 units.p done per hour 30 units and q done 24 units and r done 20 units per hour.
Now three worked per 2 hr i.e 2(30×24×20)=148 units, remaining=240-148=92 units.
Now p left so only q and r can do in 1 hr (24+20)=44 units .
If they both worked for 2hr.
i.e 44×2=88 units then the total work will finish here 92approx 88,
So, take 2 hr 11 to 2 hr means 1 P.M.
Now three worked per 2 hr i.e 2(30×24×20)=148 units, remaining=240-148=92 units.
Now p left so only q and r can do in 1 hr (24+20)=44 units .
If they both worked for 2hr.
i.e 44×2=88 units then the total work will finish here 92approx 88,
So, take 2 hr 11 to 2 hr means 1 P.M.
(3)
Divya said:
1 year ago
P=80,
Q=10,
R=12.
L.C.M = 120
P=15,Q = 12,R = 10
For 2 hours = 2*15+12+10 = 27units
The remaining 66 units are (Q+R)
Q+R = 12+10 = 22
Q+R = 66/22 = 3hours
11 A.M + 3hours = 1 P.M.
Q=10,
R=12.
L.C.M = 120
P=15,Q = 12,R = 10
For 2 hours = 2*15+12+10 = 27units
The remaining 66 units are (Q+R)
Q+R = 12+10 = 22
Q+R = 66/22 = 3hours
11 A.M + 3hours = 1 P.M.
(22)
Rose said:
2 years ago
Total work=120 units(lim of 8;10;12).
Efficiency of p-15.
“ of Q-12.
“Of R-10.
For 2 hours(9-11)all three worked = 2 *27 = 54units.
The remaining 66 units are covered by Q+R=66/22 = 3hrs.
11 am+3 hrs~ = 1 pm.
Efficiency of p-15.
“ of Q-12.
“Of R-10.
For 2 hours(9-11)all three worked = 2 *27 = 54units.
The remaining 66 units are covered by Q+R=66/22 = 3hrs.
11 am+3 hrs~ = 1 pm.
(18)
Dharmendra pandian S said:
2 years ago
P= 1 lakh = for 1 hr 12500.
Q= 1 lakh = for 1 hr 10000.
R= 1 lakh = for 1 hr 8333.
The three of them did for 9:00 am to 11:00 am so the job done is 61,666 books printed and then;
The balance they are 100000-61666 = 38,334.
So, take q +r = 18333 and try with each multiple which is near to that 38,334
18333×2 = 36,666.
So they take 2 hrs add with 11:00 then;
Answer will be 1:00 pm.
Q= 1 lakh = for 1 hr 10000.
R= 1 lakh = for 1 hr 8333.
The three of them did for 9:00 am to 11:00 am so the job done is 61,666 books printed and then;
The balance they are 100000-61666 = 38,334.
So, take q +r = 18333 and try with each multiple which is near to that 38,334
18333×2 = 36,666.
So they take 2 hrs add with 11:00 then;
Answer will be 1:00 pm.
(21)
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