Question

A certain number between 10 and 100 is 8 times the sum of its digits and if 45 be subtracted from it the digits get reversed. find the number

Answer 1

let the tens digit of no. be x
and unit digit be y
the no is 10x + y

according to question 10x + y = 8(x+ y)
10x + y = 8x + 8y
10x-8x = 8y - y
2x= 7y
y= 2x/7

so the no is 10x + 2x/7

if 45 is subtracted
10x +2x/7 - 45 = 10(2x/7) + x
10x +2x/7 - 45 = 20x/ 7 +x
(70x + 2x - 315)/7 = (20x + 7x) /7

cut 7 from both side
72x - 315 = 27x
72x - 27x = 315
45x= 315
x= 7

2x/7= 2
so the no is 72