Aptitude - Simplification - Discussion

Discussion :: Simplification - General Questions (Q.No.12)

12. 

Free notebooks were distributed equally among children of a class. The number of notebooks each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 notebooks. Total how many notebooks were distributed ?

[A]. 256
[B]. 432
[C]. 512
[D]. 640
[E]. None of these

Answer: Option C

Explanation:

Let total number of children be x.

Then, x x 1 x = x x 16     x = 64.
8 2

Number of notebooks = 1 x2 = 1 x 64 x 64 = 512.
8 8


Nagaraj said: (Aug 18, 2010)  
Anybody pls explain simply ?

Renu said: (Nov 23, 2010)  
what is x/2*16

Priya P. said: (Dec 2, 2010)  
@ Renu
x = number of student and x/2 is half of the total student as mention in question.
x/2 is multiplied with 16 bcoz its given if students number is half then each one will get 16.

hope it helps..

J K said: (Dec 24, 2010)  
why (1/8)*x^2
why x^2
x is no. of children and total books is 1/8 no. of children

Naddy said: (Jan 15, 2011)  
i have a simple way,no need any steps only logic.
first thing is the should can equally distribute.and second one is it should be divisible by8 because every child got 1/8 th of the total children. so in these option 512 is divisible by 8 and can equally distribute 512/8=64

Puja Dhamija said: (Feb 3, 2011)  
heya..
here v vil calculate the total no. of buks in 1st condtion and den in 2nd condition and eqate dem..
acc. to 1st condition,
Total no. of buks= no. of buks to 1 student have * no.of student
let no. of students= x
no. of buks 1 student have= 1/8*x
hence total no. of buks=(1/8*x)*x ............(1)

acc. to 2nd condition,
no. of students=x/2
no. of buks 1 student have=16
hence total no. of buks=(x/2)*16 .............(2)
nw from (1)&(2) equation,
(1/8*x)*x=(x/2)*16
on solving we get x=64
nw you can calculate total no. of buks from any 1 or 2nd equation
frm 1st equation
total no. of buks=(1/8*x)*x
=(1/8*64)*64
=512
thnks..I hope now every1 can get logic..!!

Adarsha said: (Aug 7, 2011)  
Thanks puja for the logic.

Santhosh said: (Oct 22, 2011)  
Thanks puja :).

Sanat said: (Apr 5, 2012)  
@Puja.

You have simply told about the logic. It is simple, but You haven' t told why we equate them? why the total no of books in 2 cases will be same. ?

Saranya said: (May 4, 2012)  
Nice explanation puja.

T.B said: (Aug 28, 2012)  
Heya..
here we will calculate the total no. of buks in 1st condtion and den in 2nd condition and eqate dem..
acc. to 1st condition,
Total no. of buks= no. of buks to 1 student have * no.of student
let no. of students= x
no. of buks 1 student have= 1/8*x
hence total no. of buks=(1/8*x)*x ............(1)

acc. to 2nd condition,
no. of students=x/2
no. of buks 1 student have=16
hence total no. of buks=(x/2)*16 .............(2)
nw from (1)&(2) equation,
(1/8*x)*x=(x/2)*16
on solving we get x=64
nw you can calculate total no. of buks from any 1 or 2nd equation
frm 1st equation
total no. of buks=(1/8*x)*x
=(1/8*64)*64
=512

Joe said: (Sep 26, 2012)  
@Sanat - Please read the question carefully. @Puja - Thanks.

Salil Shete said: (Jun 18, 2013)  
Case 1:

X is no of student.
No of books to each student= X/8.

therefore,
Total no of books = X * X/8.

Case 2:

If no of student is half = X/2 .
Each student will get 16 books.

Total no of books = 16*X/2.

Case 1 and 2.

X*X/8 = 16*X/2.
X = 64.

Case 2 : Total no of books = 16 * 64/2 = 512.

Lakshmi said: (Jul 24, 2013)  
Why should we equate those 2 conditions?

Gugan said: (Dec 9, 2013)  
@Lakshmi.

Both the conditions are related to Total no of books. Hence they are equated.

Swapna said: (Dec 31, 2013)  
No of children = (1/2)x = 16.

=> x = 32,

So the no.of children is 32 then the no of notebooks is:

32x16 = 512.

Satyapravallika. said: (Dec 29, 2014)  
@Swapna.

I couldn't understand your logic. Please explain me.

According to the question, if no.of children are halved then each student gets 16 books.

Then how we will equate both?

Sibhi said: (Dec 30, 2014)  
As per the above calculations made by others if the total number of students are 64, then half the students when multiplied with 1/8th of them will be equal to 4.

But in question it is give as 16. All the above answers are wrong. Total number of students will be 256 and total number of books will be 8192 books.

Mohit Bansal said: (Sep 17, 2015)  
If class is half student get half books compared to full class.

So full class strength is 32*8 = 256.

And total number of books distributed are 8192.

As simple as that first time looking and wrong question in Indiabix.

And look people are giving explanations that are totally vague what they are doing is equating half strength one side with full strength another side.

Before typing such explanations one should be clear in his own calculations.

Ganesh said: (Sep 28, 2015)  
@Mohit.

Same thing for you as well. Question and explanation are correct in Indiabix. First you understand and then comment.

Prabhath said: (May 30, 2016)  
Case I:.

Number of children = C.
Number of books each child got = C/8.
So, total number of books B = C * C/8 = C^2/8.

Case II:.

Number of children is reduced to half = C/2.
Now the number of books each child gets = 16.
So, total number of books B = C/2 * 16 = 8C.

In both cases the Total number of books distributed are same.

So, C^2/8 = 8C.

Solving we get C = 64.

That gives.

Total number of books B = 8C = C^2/8 = 512.

This is the conventional method. For short-cuts refer the above given explanation.

Jay Negi said: (Jun 27, 2016)  
512/ 16 = 32.

It 's half of the total no. 32 * 2=64.
512/64 = 8 it's dived to total no of children & 64 * 1/8.

Lobita said: (Jul 11, 2016)  
Why (1/8)x taken in the solution?

Ishika Gupta said: (Sep 13, 2016)  
Let number of children be x.

Then it is given that 1 child got 1/8 of no of children i.e.1/8 of x which means x/8.

Now if 1 child got x/8 then total number of notebooks

Or x children got (x/8) * x = x^2/8, Eqn --->1.

In second case number of children is half i.e. x/2.

1 child got 16 then x/2 got = 16 * x/2 = 8x, Eqn --->2.

Now we have 2 expressions.

1) 8x.

2) x^2/8.

Both are equal since both represent the total number of notebooks.

Equating them.

8x = x^2/8.

x^2 = 64x.

x = 64.

Put this value in anyone 1 or 2.

The total number of notebooks = 8 * 64 = 512.

Babi said: (Nov 21, 2016)  
Let, total no of students = x,
books allotted to each is = x/8,
Total no of books is = x * x/8 = x^2/8.

Now, is total students is halved i.e = x/2.
Books will be allotted to each is = (x/2)/8 = x/16.
Which is given = 16.
x/16 = 16
x = 256 ---> (i).

Now, the total number of books = (x^2)/8.
Putting the value of x gives 8192.

Correct me guys. if I am wrong.

Sandeep said: (Nov 27, 2016)  
Thanks @Salil.

Viswa said: (Mar 17, 2017)  
@Swapna.

Thanks for the simple way of solution.

Surya said: (Aug 18, 2017)  
@ALL.

Each student has 16 books i.e total students are 16*8=128
It is said students are halved i.e we to double it 2*126=256>> actual number of students.

Each student gets books equal to 1/8 of total class strength 256/8=32>> actual number of books each student gets.

Total books distributed are 32*256=8192.

Tell me if I am wrong.

Ramjay said: (Sep 2, 2017)  
Here we should understand that total number of books is constant in both conditions. Let total no. Of student is X and therefore total.

No of notebook is X * X/8= X/2 * 16.
Here X=64.
Here we get total no of the student.
Therefore total no of note book is 64 ÷ 64/8= 512.

Vivek said: (May 11, 2018)  
Thanks everyone for giving the explanation.

Rajiv said: (Aug 14, 2018)  
@All.

As per my calculation;

x is no of students.
16*2= no of books per student in the whole class.
32=x/8.
x=32*8.
Total no of books= x* x/8.
= 32 * 8 * 32 * 8 /8.
=1024*8.
=8192.

Nikita said: (Feb 11, 2019)  
Thank you @Salil.

Vaibhav Pal said: (Jun 12, 2019)  
I agree, the correct answer is 512.

Raghavendra Naik said: (Aug 18, 2019)  
Since we have 2 unknow;

No of student = x.
No of books = y.

Find when a student is x/2.
y=x/8(from 1st sentence)
16 = x/2/8.

x = 16 * 16 = 256.

So 2 * 256 = 516(since we are done last calculation for half reduced student strength, here we are calulating for complete strength )

Apoorva said: (Oct 30, 2020)  
Yes, right @Surya.

The Correct answer is 128.

Blashee said: (Feb 8, 2021)  
Let no. of children= x

The third line of the problem says:
Had the no. of children been half, means- x/2, then each child would have got 16 notebooks means- x/2=16.

So, x=32(these are only half of the children), then total children= 32x2= 64 children.

The second line of the problem says:

The no. of notebooks each child(i.e 1 child) got was 1/8 of the no. of children, means-
1/8 of 64= 8 notebooks,

So, if 1 child got 8 notebooks, then 64 children got 64x8 = 512 total notebooks.

Anonymous said: (Aug 1, 2021)  
Can someone explain how 64 was obtained after solving the equation?

Anonymous said: (Aug 23, 2021)  
We should know that Total no of the book is same for both the case. It's just that the no. Of books received by each std is different.

For full strength of STDs.
Book received individually = 1/8 of x.
where x = total students.
Total no. of books = 1/8 of x * x.

For half strength of stds;
We know total std is x, so half std means x/2.
Total books = total std * 16 ( book received individually).
We know for the second case total std is half(x/2) so;
Total books = x/2 * 16.

So now we know that total no. Of books is same for both the case.
Thus equating the equ for total no of books:
1/8 of x *x = x/2 * 16,
We get x = 64,
Hence the substituting x, we get 512 as the total no of books.

Abhik Kumar Majhi said: (Aug 27, 2021)  
256 will be correct.

256/2= 128,
128/8 =16 (as per given problem).

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