Aptitude - Time and Work - Discussion

18. 

Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?

[A]. 7 hours 30 minutes
[B]. 8 hours
[C]. 8 hours 15 minutes
[D]. 8 hours 25 minutes

Answer: Option C

Explanation:

Number of pages typed by Ravi in 1 hour = 32 = 16 .
6 3

Number of pages typed by Kumar in 1 hour = 40 = 8.
5

Number of pages typed by both in 1 hour = ( 16 + 8 ) = 40 .
3 3

Therefore Time taken by both to type 110 pages = ( 110 x 3 ) hours
40

= 8 1 hours (or) 8 hours 15 minutes.
4


Pandu said: (Jan 23, 2011)  
How to calculate the 8 1/4 hours= 8 hours 15 minutes.

Mahesh said: (Feb 4, 2011)  
1 hour mean 60 minutes
1/4 hour mean 15 minutes
1/2 hour = 30 minutes

Mani said: (Apr 11, 2011)  
33/4

8.25

0.25 *60 = 15

Ramu said: (Sep 22, 2011)  
Why did they change 40/3 into 3/40 in the next line. ?

They could have done like 110*(40/3) itself. !

Ashwin said: (Oct 9, 2011)  
No of pages typed/Hours=40/3/1=40/3-----First case
No of pages typed/Hours=110/x-----------second case

The ratio would be same in both the cases

40/3=110/x
Therefore

x=110*3/40=8*1/4 hrs

Navena said: (Apr 18, 2012)  
How do you solve 16/3+8 ?

Kunu said: (Apr 27, 2012)  
@Navena
16/3+8=
16+24/3= 40/3(LCM 3)

Krittika said: (Aug 31, 2012)  
Why can't I do like this?
32 pages r typed by Ravi in 6 hrs
1 page is typed in 6/32=3/16 hrs.
similarly 1 page typed by kumar is 1/8 hrs.
then 1 page typed by both of them in (3/16+1/8)=5/16 hrs.
So 110 pages typed by them in 110 * 5/16 hrs = !!?

Nitin. said: (Oct 12, 2012)  
If you solve 110*3/40 you will get exactly 8.25. Then why 8.15 please anyone explain in detail.

Sunny said: (Feb 17, 2013)  
I did the following steps but the answer I am getting is 8.25:
Ravi takes 6 hrs to type 32 pages.
For one hour he will type:32/6=16/3 pages.
Kumar takes 5 hrs to type 40 pages.
For one hour he will type:40/5=8 pages.

So,for one hour kumar and ravi type (16/3+5) pages i.e. 40/3.

1 hour---40/3 pages.
? ---110 pages.

Do cross multiplication and you will get answer.

Kishore said: (May 3, 2013)  
@Krittika.

Your method is not correct. It can be explain with a simple example.

Suppose ravi type 1 page in 1 hr.
Kumar type type 1 page in 1.5 hr.

If they work together, 1 page type by both can not be 1+1.5 = 2.5 hr (combined effort should reduce the time but here its opposite).

I hope you get it.

Amansamana said: (Aug 12, 2013)  
Hey guys why should direct count total unit, like,

Ravi 6* 32 = 192.

And kumar unit 5 * 40 = 200. But solving by that answer will be approximately 9, so anybody can tell, what is the mistake in that method?

Sumit Vyas said: (Jun 28, 2014)  
(16/3+8) = 40/3 how can simplify this equation?

Divya said: (Sep 16, 2014)  
@Kishore.

Can you please explain your example in a detailed manner.

How do you assume that ravi takes 1 hr to type 1 page and kumar takes 1.5 hrs to type 1 page.

Anil said: (Jan 7, 2015)  
1 hr = 60 minutes.
0.25 hr = x.
Cross multiplication.
60*0.25 = 15.

Mohammed Ashraf said: (Jan 11, 2015)  
Here is the easy step guys.

No. of pages typed by Ravi in 6 hours = 32.

Therefore no. of pages typed in 1 hr = 32/6 = 16/3.

No. of pages typed by Kumar in 5 hr = 40.

Therefore no. of pages typed in 1 hr = 40/5 = 8.

No. of. pages typed together in 1 hr = (16/3+8) = 40/3.

So, 40/3 pages were typed in 1 hr.

Therefore 110 pages will be typed in 1*110/(40/3) (by cross multi).

= 3 110*3/40 hours.

Hope you will get it.

Vivek said: (Jun 7, 2015)  
How will you get 8 1/4 when you multiply 110*3/40?

Gnanamayil said: (Jul 1, 2015)  
K but one doubt if we take days or works in time and work we take like 5 days means we put 1/5 but here why we take directly without denominator like 8 as 8 not 1/8. Please explain me.

Ranji said: (Oct 2, 2015)  
D is the option C is incorrect it comes as 8.25 hrs and not 8.15 hrs.

Khoshali said: (Oct 9, 2015)  
Isn't 8.25 is the right answer?

R: 1 hour = 32/6 pages.

K: 1 hour = 40/5 pages.

Let us assume they worked for x hours to complete the work.

[32/6+40/5]x = 110.

[160+240]x/30 = 110.

400x/30 = 110.

x = 8.25.

Pritam Kumar said: (Jan 18, 2016)  
Every step is correct till the last. Only calculation mistake is there. It's answer should be option D: 8 hours 25 minutes.

Kaushal said: (Mar 17, 2016)  
Yes its answer should be D.

Kumar Abhishek said: (May 7, 2016)  
How the answer is option C?

The correct answer is 8 hours 25 minutes.

Ankit said: (Jun 10, 2016)  
Yes, answer id 8 hours and 25 minutes.

Because it is 33/4, which is equal to 8 * 1/4, not 8 + (1/4). Understand this point.

Harsh said: (Jun 29, 2016)  
Assume that the both took X house to complete the job and from the question, we know that Ravi types (16/3) pages in an hour while kumar types 8 pages.

So, ((16/3) * X + (8) * X) = 110.
Solve to get X = 8.25.
Where 0.25 of 1 hour is 15 mins,
so, X = 8 hrs and 15 mins.

Kavi said: (Jul 9, 2016)  
Here 3/40 * 110 is given 8.25. But we have the 0.25 value so it is converted to minutes 0. 25 * 60 = 15.

So the answer becomes 8 hours 15 minutes.

Thank you.

Milon said: (Aug 14, 2016)  
Anybody know the quick method to solve this type of problem?

Mahi said: (Aug 28, 2016)  
33/4 = 8.25 not 8.15.

Kalai said: (Sep 14, 2016)  
Yes, the right answer is 8.25mins.

Kranthi said: (Oct 21, 2016)  
Answer 8.15 min.

After all calculation, we get 8.25.

Now 8 hours take beside,
.25 = 25/100 = 1/4.

If we convert 1/4 in min it's 15 min ( 1/4 * 60).
Now answer 8.15 min.

Abhi said: (Dec 16, 2016)  
Why 40/3 is taken as 3/40? Not getting this, please help me.

Tara said: (Dec 31, 2016)  
@Ranji.

The answer 8 hours and 15 minutes is CORRECT. The error you are overlooking is the number 0.25. In you answer, mathematically it comes to 8.25, yes, but remember that means 8 hours and 0.25 hours. 0.25 hours is basically a quarter of an hour which is 15 minutes.

Arunkumar said: (Jan 27, 2017)  
Convert hr to min .

Ravi's one min work = 32/360 = 4/45 (6 hours = 360 min).
Kumar's one min work = 40/300 = 2/15 (5 hours = 300 min).
4/45 + 2/15 = 10/45( ravi + kumar one min work).
So, for 110 pages 110(45/10) = 495 mins ==> 8 hrs(480 min) + 15 min ==> 8hrs 15 min.

Vikas Baba said: (Jun 1, 2017)  
Please, tell me that why we not required of remaining work = 1-40/3 =37/3?

Lieja said: (Jun 26, 2017)  
No need to find remaining work. They asked to find only how much time to complete the 110 pages. So total pages done by both (40/3) * 110.

Rahul said: (Sep 17, 2017)  
Please tell me the calculation of (110 x 3/40).

Piyush said: (Oct 28, 2017)  
@Amansamana.

Ravi-192
Kumar-200
And applying lcm is not right approach as work is not same in both the cases.
so solution given is best for this type of question.

@Rahul
40/3 pages together in 1 hour.
1 page together in 3/40 hour.
110 pages in (110 x 3/40).

Pooja said: (Jan 10, 2018)  
1/4*60 => 15 min.

Annapurna Kashyap said: (Feb 7, 2018)  
Elan's 1 hour work = 40/5 =8.
Elan's 6 hour work = 8*6 = 48.
Pages written by Ronald and Elan in 6 hours = 48+32 = 80.
( M^1*H^1/W^1=M^2*H^2/W^2).

2*6/80=2*x/110 (as x is the no of hours taken by both to write 110 pages).
= x=33/4= 8hours and 15 min.

Rahul said: (Nov 23, 2018)  
8.25 hr means 8 * 60 min + .25 * 60 min.
.25 *60 min = 15 min.

That is why the answer is 8 hr 15 min.
or
8.25* 60 = 495,
80*60=480,
495-480=15 min.

Navya Sri said: (Nov 10, 2019)  
Can any one explain me that why you multipled with 3/40 with 110. But we got 40/3 for 1 hour.

Neeraj said: (Apr 3, 2020)  
Time taken by Ravi for typing 32 pages=6hours.
Time taken by Kumar for typing 40 pages=5hours.
Therefore, time taken for Ravi for typing 1 page=6/32.
Similarly, time taken by Kumar for typing 1 page=5/40.
So, time taken when both worked together for typing 1page= (6/32) + (5/40).

Time taken when both worked together for typing 110 pags=110* ( (6/32) + (5/40)).

Is this method valid? Anyone suggest me.

Himanshu said: (Jun 10, 2020)  
Ravi typed 32 pages in 6 hrs that mean in one hour he typed 6 pages.
Kumar typed 40 pages in 5hrs that mean in one hour he typed 8 pages.

If they both work together they can type 8+6=14 pages per hour.
Now they have to type 110 page and they can type 14 page per hour.
110/14 = 7.85 =7 hrs and 85 min =8hrs and 15 min.

Pema said: (Oct 30, 2020)  
@Himanshu,

Your method is very simple and clean, thanks.

But 32/6 gives you approximately 5.33.

Following your steps, the answer is option D. Which is 8hours:25mins. Please check it.

Ladshika Mohan said: (Nov 10, 2020)  
3*110/40 = 8.25 then how come 8.15?

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