Let x be the digit in units place. Digit in ten’s place is then 15 - x. ∴ The number = 10 (15 – x) + x The new number with reverse digits = 10 × x + (15 – x) ∴ 10(15 – x) + x + 9 = 10x + 15 – x ⇒ 150 – 10x + x + 9 = 9 x + 15 ⇒ 18x = 144 ⇒x=
144
18
=8 The digit of ten’s place = 15 – 8 = 7 ∴ The required number = 78.