Aptitude - Simplification - Discussion

@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.

Thank you @Salil.

I agree, the correct answer is 512.

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 )

Yes, right @Surya.

The Correct answer is 128.

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.

Can someone explain how 64 was obtained after solving the equation?

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.

256 will be correct.

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

Thanks a lot @Dhamija.