Aptitude - Time and Work - Discussion

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

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.

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=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.

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 = 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).

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.

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.

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.