Aptitude - Time and Work - Discussion

Simplest calculation: quite long because only logic is used in this solution.

One lakhs books is to be printed okay and each machine prints the same number of books but on different hours so iF machine.
A takes 8 hours to print one lakh books so.
No of books printed in an hour by A = one lakh/8 =12500 books is printed in an hour.
And A worked for two hours so it will print 25000 books.
And now machine Q will take 12 hours to print one lakhs books.
No of books printed in an hour by q = one lakh/ 12 = approx 8333 books for one hour.
For two hours it ill print 16666 approx books.
And machine are will take 10 hours to print one lakh = one lakh/ 10 = 10000 books for an hour.

So for two hours, it will print 20000 books.
So till 11 am the number of books printed is 25000+16666+20000= approx 61666 books.
Remaining books to be printed is 100000-61666.

Add remaining books from other machines from q and are and count no of extra hours added to make the count one lakh.

Hi Friends,

1) P worked from 9 AM to 11 AM (2 hours of work time).

2) In two hours it can print 25,000 books ( Since, 100,000 books in 8 hours it can Print)

3) So remaining 75000 books has to be printed by other two machines (Q and R).

4) Compute the capacity of Q and R, viz : Q+R = ((1/10)+(1/12))= 11/60 = 5.45 hours.

5) So lets put ourself a question. Both the machine needs 5.45 hours to Print 100,000 books. But already 25,000 books has been printed by Machine P. To print remaining 75,000 books Q and R will be needing approximately 4 hours.

Viz; Let x be the number of hours required by Q and R to print 75,000 books.

x = [(5.45*75,000)/100,000] = 4 hours (approximately).

6) All the machines started at 9 Am. Hence 9 + 4 = 13 (1.00 pm).

Hi friends... In this problem it is having some confusion in the last step....i will explain that step in a easy way....

The work completed by q and r after closing of p machine is
23/60....
but we don't know the time...
we have to calculate it...

(q+r)'s 1 hour work = 11/60.

we can represent the above relation like this....

11/60 (portion of work)-------> 1 hour (time)

23/60 (portion of work) ------> ....? (time)


By cross multiplying the above terms we will get.

11/60 * 60/23 = 23/11

that is approximately equals to 2 ....

q and r machines took 2 hours to complete the remaining work....

i.e.,
11+2 = 1 p.m

the total 1 lakh books will be printed by 1 p.m

Hey guys I used a logic mite be correct or not I don't know!

As we know p works for 8hrs, q works for 10hrs and are works for 12hrs so there is difference of 2hrs. Where p complete the works for only 2hrs in time 9am to 11am. In the same time the remaining q and are also works but we observe by comparing q works more than 2hrs so if the q started at the same time where p started then q finish the work at 11am but where as are who work for 4hrs more than p. So in the time of he started he also completes the work at 11am but remaining 2hrs he need to work so the work will be finished at 1pm i.e. (11am+2hrs).

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

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.

Ok, since work done is the same for all the machines,( to print 1 lakh papers) you can assume any number to be your work done, cleverly you always assume the LCM of time given.
LCM of 8,10 and 12 is 120).

So let the work is to print 120 papers.
Given;

MACHINE ---- TIME ---- efficiency
P ---- 8 ---- 15
Q ---- 10 ---- 12
R ---- 12 ---- 10.

Now P works for 2 hours, So it will print 30 pages, and the remaining 120-30, 90 pages will be printed by Q and R.

Therefore time taken = 90/22 = 4 hrs approx.

Therefore, the finishing time will be 1 am.

So the easiest way to solve this:

P Q R from 9 am to 11 am do work together so;
For p 1 lakh - 8hrs.
In 2 hrs - 25000 work.

For q 1 lakh- 10hrs.
In 2 hrs - 20000.

For r 1 lakh - 12 hrs.
In 2 hrs- 16666.67.

Total work done in 2 hrs.
25000+20000+16666= 61666.

Remaining work = 38334
So R+Q work from 11 am together,
Q do 10000 in an hr.
R do 8333
Together they do approx 18333 in an hr.
Hence;
In 2 hrs they do 36666 something work which is approximately equals to 38334.
So, they will complete the work around 1 pm.

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.

P takes = 8 hrs.
Q takes = 10 hrs.
R takes = 12 hrs.

We assume total work as the LCM of 8, 10, 12 = 120.

P completes 15 unit/hours.

Q = 12 unit/hrs.
R = 10 unit/hrs.

P+Q+R together = 37 unit/hours.

They continue to work for 2 hours i.e. 37x2 = 74 unit is completed.

Remaining work = 120-74 = 46 units.

Remaining work is done by Q and R,

So, P+Q = 22 unit/hours.

They will take 2 hours more to complete remaining work.

22x2 = 46 units.

Work will complete in total 4 hours.

So, at 1:00 PM.