Question

A group of 630 children is arranged in a row 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 ?

Answer 1

Let the no. of students in front row be x.
So, the no. of students in next rows be x–3,x−6,x–9 ... so on
If n i.e. no. of rows be then no. of students (n=1)
x+(x–1)+(x–2)=630
3x=633
x=211
If n i.e. no. of rows be then no. of students (n=3)
x+(x–3)+(x–6)=630
3x=639
x = 213
So possible,
Similarly for n = 4
x+(x–3)+(x–6)+(x−9)=630
4x–18=630
⇒ x=162

If n = 5
(4x–18)+(x−12)=630
5x–30=630
x=120
Again possible.

If n = 6
(5x−30)+(x−15)=630
6x−45=630
6x=675

x ≠ Integer
Hence n ≠ 6

so 6 number of rows in not possible

Answer 2

Answer:

Let no of children be x, x+3,x+6,x+9,x+12,x+15...........

Present in Rows

,.......... respectively

Putting R=3,4,5 and 6

We see that when R=6

x+x+3+x+6+x+9+x+12+x+15=630

6x+45=630

6x=585

x=97.5

then x is not an integer.

So, R=6 does not satisfies.