Verbal Reasoning - Arithmetic Reasoning - Discussion

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?

12 * 8 = 96
No of students = 12.
4 students did not turn up, So,
12 - 4 = 8.

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.

Let option A, that 8 students joined picnic and the eatable price is 96Rs. According to question, 4 of them didn't turn up, so the total no of the remaining students are 4, if we divide 96/4=24 rs.

If we contribute this money to 4 students it will be 96 which is the total price, hence option A is correct.

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.

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

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.

The answer must be wrong let's see for option A) 8.
Total number of people = 8.
Money to be invested by each if all had come = 96/8 = 12.

now 4 people didn't come then the number of people = 8 - 4 = 4
now 4 of the remaining had to invest an extra 4 each so new investment = 12 + 4 = 16 and then if four collected 16 then the total = 16 * 4 = 64!= 96.
So 8 is the wrong answer.

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).

I think 12 is the answer.