Aptitude - Simplification - Discussion

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.

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.

Why (1/8)x taken in the solution?

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.

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.

Thanks @Salil.

@Swapna.

Thanks for the simple way of solution.

@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.

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.

Thanks everyone for giving the explanation.