Question

For a two-digit number, one’s place is 3 more than its ten’s place. The product of this number and its digit sum is square of double the digit sum. What is the number?

Answer 1

Digits: x, x+3

Number: 10x + x + 3 = 11x + 3

Product of the number and digit sum: (2x + 3)

(11x + 3) = (4x + 6)²

22x² + 39x + 9 = 16x² + 48x + 36

6x² - 9x - 27 = 0,

2x² - 3x - 9 = 0

(-ve being a fraction not acceptable)

Number = 36