Aptitude - Time and Work - Discussion

We can also do by this method,
Lcm of 8, 10 and 12 is 120.
Suppose total work is 120.

Then, 120/8 = 15.
120/10 = 12.
120/12 = 10.

Now above are respective capacities and we know that work = capacity x time
Hence we have,
15x2+12x+10x = 120.
22x = 90
x = 4 answer.

Why we didn't add the P's work at the end? Please explain.

As P works for 2hrs that is 9 am to 11am.

Consider for 2hrs
1lakh is done in 8hrs
2hrs..??

(2*100000)/8 = 25000.

Same for Q and R.

(2*100000)/10 = 20000 --->Q.
(2*100000)/12~~16000 --->R.
25000 + 20000 + 16000 = 61000.

In 2 hrs total books are printed are 61000
100000 - 61000 = 39000.

Remaining work is 39000.
Q+R work in 2hrs.
Q+R = 20000 + 16000 = 36000.
Approximately within 2hours Q and R can complete a work.

Total work needs to be completed = lcm (8,10,12) = 120 work.
Efficiency of P (work completed in 1 hr) = 120/8=15 work.
Similarly for Q=12 work and for R = 10.
Total work done by all the three in 1 hr =15+12+10 =37.
From 9 to 11 am all worked together ie. 37*2 =75 work completed out of 120.
Remaining work =120-75 = 45.
Work completed by Q and R in 1 hr = 10+12 =22.
Time taken to complete 45 work ==> 45/22 ~ 2 hrs.
ie.11 AM + 2 hrs ==> Around 1 PM work will be finished.

I think we can do like this!

We need to find (Q+R) Work ! Since, We can write it as,
(Q+R ) = (P+Q+R ) - P ---> 1.

Therefore , P+Q+R = (1/8)+(1/10)+(1/12) = 37/120.
All of them Printed for 2 hrs, So (37/160) * 2 = 37/60.
Now find the Individual Work done by P,
P= (1/8), for 2 hrs (1/8)*2 = 1/4.
1--> (Q+R) = (37/60) - (1/4) = 11/30.

Therefore Taking, 30/11 = (approximately 2 hrs).
11 hrs + 2 hrs = 1 PM.

I hope this will be Easy to Understand!

I didn't understand @Sukanya.

The solution is;

10 - 8=2
12 - 10=2
So, two is a common difference.
Then, P is closed at 11:AM.
11:00 + 00:30 = 11:30.
Continued for four good times then you'll get 1:00PM.

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.

Very easy approach.

Work to do (W) -> print 1 lakh books.
Machine P can do that work W in 8 hours.
Machine Q can do that work W in 10 hours.
Machine R can do that work W in 12 hours.


All machines started at 9 AM means all Machines P,Q and R are working together till 11 AM, meaning 2 hours together
So we write W/8 +W/10 +W/12, which together gives us per per-hour work (print) of each machine
->they did that together for two hours, so we multiply it by 2
2(W/8 + W/10 + W/12).

P is switched off at 11 AM means now remaining to machines Q and R will do the remaining work.
(W/10 + W/12)

But for how long these remaining machines are doing this remaining work, let's say x hours.
x(W/10 + W/12).

So total.

2(W/8 +W/10 +W/12) +x (W/10 +W/12) = W = total work.
solving for x , we get;
x ~= 2 hours.
Machines started from 9Am to 9Am + x time. So we get 1 AM as an Answer.

All the machines are started at once.
we have got the solution as 4 hrs for both machines q & r
they have started at 9 a.m.
q & r work for 4 hrs

So 9+4=13 i.e,1 p.m.