**Q.)A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?
**(I)3 (ii)4 (iii)5 (iv)6 (v)7

SOLUTION:

Let the number of students in the front row be x.

And no of rows=n.

Hence, the no of students in the next rows would be

(x-3), (x-6), (x-9), ………….and so on.

If n , i.e., no of rows be 3, then number of students

=x + (x-3) +(x-6) =630

=>3x = 639 =>x=213

Likewise if n=4

x + (x-3) +(x-6) +(x-9) =630

=>x=162

Likewise if n=5

x + (x-3) +(x-6) +(x-9) +(x-12)=630

=>x=132

If n=6, then

6x = 675

So, n=6 is not possible.

Option(iv)