Aptitude - Time and Work - Discussion

14. 

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

[A].
5 5
11
[B].
5 6
11
[C].
6 5
11
[D].
6 6
11

Answer: Option A

Explanation:

P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

P's1 hour's work = 1 and Q's 1 hour's work = 1 .
96 80

(P + Q)'s 1 hour's work = 1 + 1 = 11 .
96 80 480

So, both P and Q will finish the work in 480 hrs.
11

Number of days of 8 hours each = 480 x 1 = 60 days = 5 5 days.
11 8 11 11


Hanmant said: (Jun 1, 2010)  
How come 11/480?

Suresh said: (Jun 9, 2010)  
How come 5 5/11 days from 60/11?

Deepak said: (Jun 16, 2010)  
How come 11/480?

Manisha said: (Jun 30, 2010)  
11/480 is the addition of 1/96+1/80
(1*5)/(96*5)+(1*6)/(80*6)=5/480+6/480=11/480

Asha said: (Jul 8, 2010)  
When we divide 60 by 11 the quotient is 5 and the remainder is 5 11 is the divisor? so 5 5/11.

Nagu said: (Jul 12, 2010)  
Hi all

we can write 60/11 = (5*11+5)/11
= (55+11)/11

it is same as 5 5/11 here first first 5 is quocient and senocd 5 is remainder and 11 is deviser

Neha said: (Aug 1, 2010)  
Why multiplied by (1/8)?

Rani Maria said: (Aug 3, 2010)  
Take the LCM of 96,80 then we get 480.
then 1/96 * 480 + 1/80 *480 = 5/480 + 6/480 = 11/480.

Chintan said: (Aug 7, 2010)  
Neha. . They work to gather 8 hours in 1 day that is shown in que. So ans mult. By 1/8

Supriya said: (Aug 22, 2010)  
How can we solve this 480/11 * 1/8..and how came the ans 60/11 ?

Srinivasareddy said: (Aug 31, 2010)  
P can do the work in 12days. He do per day 8 hours.

P can do work in total hours is:96.

Same as Q can do work in:80hours.

P's one day work is:1/96.

Q's one day work is:1/80.

P+q one day work is:1/96+1/80=11/480.

P+q work is:480/11.

P+q can done 8 hours per day:480/11*1/8.

Srikanth said: (Sep 7, 2010)  
Why should we take 11/480 as 480/11 ?

Akila said: (Sep 17, 2010)  
11/480 is the part of work completed in 1 hour.

If we reverse it we can get time.

Sagarika said: (Oct 3, 2010)  
We can do this by taking up the lcm of both's working hours to complete the task i.e., of 96 and 80 which comes to be 480.

So if the whole work is considered to be 480parts then P can complete in 480/96=5 days and Q can in 480/80=6 days and if they work together then 480/(5+6) days.

If they work 8 hours each then

=(480/11*1/8) days

= 480/88

= 5.454545.. or 5(5/11)

Shridhar said: (Nov 26, 2010)  
Sagarika your explaination is very nice.

Shekha said: (Dec 10, 2010)  
Sagarika your explanation is very simple. And Rani maria thanks for thinking me simple.

Sikha said: (Dec 18, 2010)  
Why multipled by 1/8 not 8?

Anshik said: (Jan 12, 2011)  
Why multiplied by 1/8 and not 8 ?

Nagarjun said: (Jan 14, 2011)  
@sikha,anshik
for 1 day they work 8hrs
for x days they work 480/11 hrs
so x=(480/11)*(1/8)
thats it....

Sourya said: (Jul 18, 2011)  
They worked 8 hours for 1 day
" " 1 " " 1/8 day
So, 480/11 " " (480/11)*1/8 day= 60/11 days= 5 5/11

Deeps said: (Aug 17, 2011)  
Why should we take the reverse of 480/11 and multiply?

Why shouldnt we directly multiply?

Sush said: (Aug 26, 2011)  
@Deeps

For 1hr-11/480th part of work is done.

So, to complete whole work it'll take 480/11hrs.

Eg:
For 1hr-1/4th f work
For xhr-1(whole) work..? x=4hrs.

Just take it to the l.h.s from r.h.s thats it.

Hope you are clear now...:)

Asha said: (Sep 16, 2011)  
Ok now look at the theorem. as per the theorem if A does a work in x days and B does the same work in y days then total no of days taken by A&B to complete the same work is xy/x+y

Now for the question the equation would be (12*8)*(8*10)/ 12*8+10*8= 480/11

The answer obtained is in hrs, to convert this in no of days divide it by 8 as A/B does the work 8hrs in a day, now the answer becomes 60/11 which is the required answer..

Hope this will clear all the doubts.. :)

Jitendra Gupta said: (Mar 28, 2012)  
We can simply do the following!

Convert both the person's work into days bringing the same hours/day so the Man Days remain unchanged!!

Where P works 8 hour/Day working 12 Days= Man Days 96

Where Q works 8 hours / Day working 10 days= Man days 80


Now 1/10 + 1/12

So 11/60 per day work by both

so 60/11 = 5 5/11

Baljeet said: (May 1, 2012)  
Good jitendra.

Dileep said: (Aug 23, 2013)  
Given p can complete the work in 12 days working 8hrs a day.

i.e p - 12 days - 8 hrs.

lly, q - 8 days - 10 hrs (or) 10 days - 8 hrs.

Thus, p+q - x days - 8 hrs.

Hence p + q = 1/12 + 1/10.

= 22/120.

= 11/60.

Therefore p+q can complete the work in 60/11 days.

Vijay Anand C said: (Oct 2, 2013)  
P can complete work in 12 days. So for one day he completes 1/12 work. But for one day he works only for 8 hours.

Similarly Q can complete work in 8 days. So for one day he completes 1/8 work. Q works 10 hours a day.

in question they have asked in how many days P and Q can complete the work if they work for 8 hours a day.

So for P already the given work is 8 hours a day and for Q it is 10 hours a day.

So just convert Q's work into 8 hours a day. The conversion is as follows

Q for one day he works for 10 hours and can complete the work in 8 days.
Q= 1/8 for 10 hrs.

Then for one hour it is (1/8)/10.
Q=1/80 for 1 hour.

So for 8 hours it is (1/80)*8= 1/10.
Now P+Q= 1/12+1/10.

Total work is 11/60.

So they can complete the given work in 60/11 days or 5 5/11 days.

Sumasree said: (May 15, 2014)  
@Vijay Anand.

Here total work is 11/60, but how 60/11 days can anyone please clarify me?

Deepak Patgar said: (Aug 23, 2014)  
B works for 10 hrs a day i.e 2 hrs more than A.
In days he works for 16 hrs more than A.
It is equal to 2 days' work of A.

If B works for 8 hrs a days he would take 8+2=10 days to complete the same work.

Work done by A per day = 1/12.
Work done by B per day = 1/10.

Work done by A and B together in 1 day = (1/12+1/10).
= 11/60.

So number of days required will be 60/11.

Deepak Patgar said: (Aug 23, 2014)  
@Sumasree.

Suppose if A does a work in 8 days, amount of work done by him in 1 day will be 1/8,

Its the reciprocal.
In the same way if both of them does 11/60 work in 1 day they will require 60/11 days to complete that work.

James Bond said: (Dec 1, 2014)  
P's total work in hours = 12 day*8 hour = 96 hr.
P's 1 hour work = 1/96.

Q's total work in hours = 8 days*10 hours = 80 hr.
Q's 1 hour work = 1/80.

Now Both work only for 8 hours a day.

P's 8 hr work = 8* (1/96) = 1/12 (P's 1 day work).
Q's 8 hr work = 8* (1/80) = 1/10 (Q's 1 day work).

Now if P and Q work together in how many days they can complete the task.

= 1/ (1/p + 1/q).
= 1/ (1/12 + 1/10).
= 1/ (11/60).
= 60/11.

= (5*11+5) /11 in mixed fraction.

Avinash said: (Mar 12, 2015)  
Why we are taking (12*8) instead of (1/12*8)? As though taken in previous sums.

Nabil said: (Apr 27, 2015)  
No need to take hours in picture because number of hours are same.

Simple ab/a+b.

Where a=12 & b=10.

Thank you.

Mishi said: (Jun 19, 2015)  
P 12 days, 8 hours = 96. Q = 8 days, 10 hours, = 80.

P works 12 days in 8 days.

Q = 80/8 = 10 days.

= 1/12+1/10 = 60/11.

Anjali Sharma said: (Jun 21, 2015)  
Very easy question no any doubt.

Archana said: (Jul 13, 2015)  
I could not understand this question can anyone explain it please.

Nagesh G S said: (Jul 25, 2015)  
The total amount work done is 480/11, but we can not divide it by 8. Because P works for 8 hours a day and Q works for 10 hours a day.

Instead we have to calculate the amount of work done by P per day + amount of work done by Q per day, The take the reciprocal.

If we do that we get:

P = 1/96*8 = 1/12 units of work per day.

Q = 1/80*10 = 1/8 units of work per day.

Amount of work done By P+Q per day = 1/8 + 1/12 = 5/24.

Therefore to complete the entire work it will take 24/5 days.

That's equal to 4 4/5 days.

Henry said: (Dec 23, 2015)  
What amount of work are they to complete?

Saniya said: (Jun 12, 2016)  
Why did 1/8 is taken in ratio but not the above hours?

Tuhinaa said: (Aug 3, 2016)  
The explanation is a bit lengthy. Is there any shortcut to solve it.

Bhagyasri said: (Mar 10, 2017)  
1-hour work of p and q is(1/12*8+1/8*10) = 11/480.
8-hours of work is (11/480)*8 = 11/60.
For example, 1 day work is 1/x days then the total number of days is x.
Similarly, 8 hours of work is 11/60 then the total number of days is 60/11.

Hariom Pundir said: (Jun 9, 2017)  
25 men take 20 days to finish some work, after every 10 days 5 men leave the work, then in how many days will the work be finished? Explain the answer.

Ash said: (Jun 23, 2017)  
Why 12*8 is taken? 12 days n 8 hrs =96hrs how it comes?

Please explain it.

Amritha said: (Aug 18, 2017)  
@Ash

For 1 day P works for 8hours, then for 12 days (Since P completes the work in 12days.), the total no of hours is 96 hours(12 * 8).

Mr. Mp said: (Aug 31, 2017)  
480/11 is the total hours taken to complete.

Now in days we want, and in a day only 8 hours is worked as said in question
so, (480/11) / 8 nothing but (480/11)*1/8.

Still confused look at this I complete the work in 40 hours, the company says I can work only 10 hours per day, so how many days it took. nothing but 40/10 or 40 * (1/10) = 4 days.

Singham said: (Nov 27, 2017)  
If the equation is multiple with 1/8, then how could be possible that the is 5*5/11?

Supriya said: (Dec 14, 2017)  
We should take as 1/12 that means 1/n for every question noo. But in this question why we have taken as 12*8, why can't 1/12*8?

Anyone explain me.

Jakrik said: (May 9, 2019)  
p to complete eating chocolate(12*8)=96hrs (work=chocolate).
q to complete eating chocolate(10*8)=80 hrs.
LCM of 96&80=480.
p->5 chocolates/hr(480/96).
Q->6 chocolates/hr(480/80).

In 1 hour = 5+6 = 11 chocolates.
8 hour =11 * 8 = 88(in one day)
Total chocolates = 480.
Days taken to complete = 480/88 = 60/11 = 5 5/11.

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