Question

The ratio of factorial of a number x to the square of the factorial of other number,which when increased by 50% gives required number,is 1.25. Find the number x?

Answer 1

let the another number be y then,
y+50% of y = x
1.5y=x
=> y= x/1.5
also,
x!/(y!)^2 =1.25
x! / [ (x/1.5)!]^2 =1.25

Answer 2

since factorial is only of integer numbers so,
x = 1.5*2*n , where n is any natural number

Answer 3

so, x! / [ (x/1.5)!]^2 =1.25
=> (3n)! / [ (2n)!]^2=1.25 where x=3n

Answer 4

then?

Answer 5

now, when n=1, (3!)/[(2!)]^2 = 1.5 which is not equal to 1.25
when n=2 , (6!)/[(4!)]^2 = 1.25
hence , x=3n=6