Aptitude - Time and Work - Discussion

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.

Please somebody help me to solve this problem in an easy way.

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.

P = 2/8, Q = (2+x)/10, R = (2+x)/12.
(2/8)+(2+x)/10+(2+x)/12 = 1.

By solving this equation we get x = 2 hrs.
so the answer is 1PM (11AM+2hrs).

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= 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.

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.

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.

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.

Thanks for the explanation @Sai Vinitha.