Aptitude - Simplification - Discussion

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.

256 will be correct.

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

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.

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 )

Let no of children be=y.

Total books distributed in case 1 would be=y*(y/8) i.e. no. of children*book got by each child.

total books distributed in case 2 would be=(y/2)*16 i.e.no. of children in case 2 (half of y)*(book received by each child which is given as 16).

equate case 1=case2.

You will get no. of children y=64.

Thanks a lot @Dhamija.

Yes, right @Surya.

The Correct answer is 128.

I agree, the correct answer is 512.

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.