Question

the sum of the digits of a two digit number is 1/8 the number if the digits are reversed the new number is 45 less than the original number .find the original number

Answer 1

let x+10y is the two digit number
according to question ,
x+y = 1/8 (x+10y)
8x+8y = x+10y
7x = 2y ------------(1)

again ,
x+ 10y - (y + 10x )= 45
9 (y - x )= 45
y - x = 5 ------------(2)

solve equation (1) and (2)
7x =2 (5+x)
=10 +2x
x= 2 and y = 7

so number is 2 +10 x 7 = 72