Aptitude - Time and Work - Discussion

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 = 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).

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.

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

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.

P - 8 d
Q - 10 d
R - 12 d -------now,LCM of p,q,r is 120.

So, P's one day hour work = 15.
Q's =12
R's. =10.

P works for 2 hours.
So, 2*15=30.
120-30=90.

Remaining work is done by Q and R = 90/22 = 4(approx).
9:00 AM + 4 hrs = 1:00 PM.

Here,

P take a time to complete the work = 8 hours.
Q take the time to complete the work =10 hours,
R take the time to complete the work=12 hours,
One hour work by PQR=15+10+12 = 37.
Now LCM =120(total unit to complete) (120 unit means 100000).

Now time taken to complete 120 unit = 37*2 (9-11)+22 (11-12)+22(12-13)=120 unit completed till 1 AM.

This problem is simple;

First, see the difference between the machine completed work it's approximately 2 hours in each machine.

So, p machine end it's work is 11 am so,
The difference is 2.
So simply add that 11+2= 1 pm.

Take lcm of 8, 10'12.

Lcm = 120 units book to be printed.
P = 120/8 = 15 units/ hour.
Q = 120/10 = 12 units per hour.
R = 120/12 = 10 units per hour.

Total units per hour=15+12+10=37 units per hour.

P+q+r work together for two hour=37*2=74 units for two hours.

Remaining work=120-72=46 units.

P and R one hour efficiency=12+10=22 units per hour.
They need how much time to finish 46 units?

46/22 = 2.09 hours.

After 11 am they need 2 hours means 1 pm approximately.

8,10,12 for this lcm 120

Assume 120 books print
Machines printing per hour
P 120/8 = 15
Q 120/10=12
R 120/12=10.

Per hour 3 machine together print books 37

Start 9 am 11 pm machine p stop the work.

2 hours all machine worked so 2 *37=74.

120-74=46 machine Q R together print in one hour 10+12=22.

So 46/22 =2.02 so 2 hours required to print remains books
After 11 am need 2 hours need so answer 1 pm.