# 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

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?

 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.

 Karina Nunach said: (May 17, 2022) 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.