Verbal Reasoning - Arithmetic Reasoning - Discussion

Discussion :: Arithmetic Reasoning - Section 1 (Q.No.4)

4. 

A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was

[A]. 8
[B]. 12
[C]. 16
[D]. 24

Answer: Option A

Explanation:


Nayaki said: (Jun 23, 2011)  
Please explain clearly the logic any one.

Shaher said: (Aug 14, 2011)  
Please explain each step clearly.

Sikandra said: (Aug 20, 2011)  
n=total no. of students.
r=rs. per student.
nr=96 i.e. r = 96/n

each students have to play 4rs. extra because 4 students did not turn up so:
(n-4)(r+4)=96
nr+4n-4r-16=96
n(96/n)+4n-4(96/n)-16=96
96+4n-4*96/n-16=96
4n*n-4*96-16n=0
n*n-4n-96=0
(n+8)(n-12)=0
n=12
n-4=8

Sonia said: (Aug 26, 2011)  
@Sikandra. Very well explaned. Thanks so much.

Parthiban said: (Nov 13, 2011)  
Please explain clearly I didn't understand.

Harshita said: (Jan 19, 2012)  
Sikander Kindly explain how it is possible.

4n*n-4*96-16n=0
n*n-4n-96=0
(n+8)(n-12)=0
n=12
n-4=8

Neel said: (Feb 27, 2012)  
Look 96..as we know 12*8=96, number of boys decrease by 4 burden increase by 4 each.

Just write (12-4)(8+4)=96 i.e. 8*12=96.
Hence who participated are.. 8.

Shobha said: (Mar 28, 2012)  
Please explain clearly once again.

Parth said: (Oct 10, 2012)  
Very well @Neel....Shobha you can simply

80+4n -4 (96/n) = 96
4n - 4 (96/n) = 16.....divide by 1/4

Then as Neel explained (n+8)(n-12) = 96

Ashish Jalit said: (Mar 16, 2013)  
Let us suppose that,
The no.of student are x & they decide to go to picnic & spend Rs. 96 in all students there for each student has to pay rupees.

96/x ( total student are x).

But 4 students did not turn up there for now each student has to pay 4 rupees extra.

96/(x-4) = 4+(96/x)

96/(x-4)+96/x = 4

96(x-x+4)/x(x-4) = 4

96 = x^2-4x

x^2-4x-96 = 0
x^2-12x+8x-96 = 0
x(x-12)+8(x-12) = 0
(x-12)(x+8) = 0
x = 12.

No. of students attend the picnic was x-4 = 8.
x-4 = 12-4.
x-4 = 8.

Rimjhim Nayak said: (Nov 30, 2013)  
Please explain each step clearly. I cannot understand any step.

Addy said: (Jan 21, 2014)  
4 that did not turn up x(x). Total of students == total money used, hence.

4x = 96 = 24.

But since each added 4rs to cover up = 4rsx4 (not turned up) = 16.

Subtract. 24 total of students - 16 = 8.

Besty said: (Jan 23, 2014)  
Quick solution:

96 = total budget.
4 = contribution per person.

Therefore, total number of person attended the picnic equals to
x-4x = 96/4 = x-4x = 24 and then subtract 4x from x which gives you 3x and therefore, 3x = 24 and x = 24/3 = 8.

8 is the total number of persons that attended. Thank you.

Ashok said: (Jan 29, 2014)  
4(x-4x) = 96.
4x-16x = 96.
-12x = 96.
x = 8.

Archu said: (Mar 4, 2014)  
Will you please explain, how it comes x square-4x-96?

Kyle said: (Oct 14, 2014)  
An unconventional way of solving it, but it's only good if you have multiple choice answers in front of you:

Step 1: 96 (total amount)/8 (Answer A) = $12 (individual contribution).

Step 2: 8 (the # of people attending the picnic) + 4 (who have left) = 12.

Step 3: 96 (total amount)/12 (initial group) = $8.

Step 4: $8 (individual contribution for the group of 12)-$12 (individual contribution for the group of 8) = -4.

Step 5: 12*8 = 96 and 8*12 = 96.

Vamsi said: (May 15, 2015)  
I want simple to solve this question.

Evezkie.Siacor said: (Jun 28, 2015)  
What kind of formula do you get? Please answer.

Karna said: (Jun 30, 2015)  
For this type of questions it is easy to verify the options.

1st option: The no. of students attended the picnic is = 8 i.e. after deducting 4 members. If the left 4 members participated then total no. of students will be 12 members and each contribution gets Rs. 8 i.e.12*8=96.

With deducting 4 members increases the contribution of Rs. 4 i.e It gets Rs. 12 as contribution to remaining 8 members i.e 8*12=96.

Therefore the option "A" is the correct answer and we may leave with this answer.

If we not get the correct answer we may check further options also.

Vikram said: (Jan 26, 2016)  
I need clarity explanation, anybody can?

Jshan said: (May 2, 2016)  
@Parth, @Addy.

How 16 come in the solution?

Jeyanthi said: (May 5, 2016)  
I'm not getting this. I need an easy method, please help me.

Muneesh said: (May 17, 2016)  
@Jeyanthi.

Sikandra's method is easy to learn and understand the problem. Please refer it.

Jothsna said: (Aug 29, 2016)  
4 students do not turn up money.

Total no of students = total money used(say)
4x = 96,
x = 96/4 = 24.

But each added 4rs to cover up remaining 4members
we have = 4x * 4 = 16.
Now total students -> 16 = 24 - 16 = 8.

Utsav said: (Sep 6, 2016)  
Let us say that Rs that should have been paid by the 4 students = 96/4 = 24rs.
As they turned up, the rest of them paid Rs. 4 extra each.
Therefore,
24 will be equal to 4 + 4 + 4 + 4 + 4 + 4,
= 4 * 6.
Therefore,
The rest of them were 6.

Then, Total students = 6 + 4 = 10.
But 10 is not given as an option.

I think 8 may be wrong because it is not given that everyone was planning to give same amount of money to make aa sum of 96.

Vinod said: (Oct 14, 2016)  
@Sikandra.

You gave a good explanation, Thank you.

Prem said: (Nov 15, 2016)  
You explained very simple and it clear my doubt, thank you @Ashok.

Rahul said: (Dec 12, 2016)  
I need a simple formula to solve. Please, someone help me.

Armin said: (Dec 27, 2016)  
Thanks for your explanation. It cleared my doubt. Thanks a lot @Sikandra.

Likhitha said: (Jan 25, 2017)  
Is there any other way to solve this question? Please tell me the shortcut method.

Sunil said: (Mar 31, 2017)  
Every person to spend 4/- then extra 4/- expended then also total value of amount is 8/- for each person.

Prithvi said: (Apr 8, 2017)  
Why every person to spend 4?

Sagnik said: (Aug 7, 2017)  
Good explanation @Sikandra.

Saiteja said: (Aug 9, 2017)  
Superb explanation. Thank you @Jothsna.

Valarmathi said: (Mar 23, 2018)  
let x be the total no.of. friends. Let each of them had to pay Rs.y for getting a sum 96.

Therefore, x*y=96.

But four of them didn't turn up, so now the number of friends are x-4.
Remaining ones contributed Rs. 4 each extra. So now each of them has to pay y+4.

Therefore, (x-4)*(y+4)=96.

Solving these 2 equations, you will get x=12.

But four of them didn't turn up, so now the number of friends are x-4=12-4=8.

Naki said: (Apr 26, 2018)  
Let x bw no of students.

4 absent--> (x-4) students
each student spends rs 4 extra ---> (x-4)*4 for total amount 96rs ---->> (x-4)*4=96 --->> x=28rs.

4 absent.

Hence, 4rs extra ----> 4*4=16rs ------->> x=24-16=12 rs for each who attended.

Now 96/12= 8 students.

Naveen said: (May 22, 2018)  
I agree with your answers.
In my point of view.
Total investment =96,
Amount divided per head =4,
T. A=96/4=24.

4 people don't participated=4*4=16,
Since 24-16=8.

Can we apply this method?

Madhu said: (Jun 7, 2018)  
Please explain this problem clearly.

Sankar said: (Oct 10, 2018)  
Total 12 members * Rs. 8 = Rs. 96/-.

If total becomes 8 members (since 4 of them left) * (Rs. 8+extra Rs4/-) = Rs. 96/-.

Shivani said: (Feb 2, 2019)  
I think 12 is the answer.

Rajesh said: (Dec 16, 2019)  
It has 2 answers both A&B.

You can go in two steps:

1. By evaluating through answers (Choices) given. Like you can cross-check those options wise.

8*12 = 96.
4*16 = 96.

OR,

12*8 = 96.
8*12 = 96.

2. Or Answer given in Explanation.

(X-12) (X+8) =0.

Then If X = 12 or X = I8I (+8).

Swathy said: (Jun 6, 2020)  
Right, Agree @Naki.

Pradeep said: (Oct 8, 2020)  
12 * 8 = 96
No of students = 12.
4 students did not turn up, So,
12 - 4 = 8.

Naresh Gyawali said: (Feb 17, 2021)  
Check 24 * 4(four extra pay per person) = 96.
96-96=0.

Check 16*4=64
96-64=32 is not the square root.

Check 12*4=48
96-48=48 is not the square root.

Check 8*4=32
96-32=64 is square of 8.

That's why the answer is 8.

Post your comments here:

Name *:

Email   : (optional)

» Your comments will be displayed only after manual approval.