Question

the sum of the digit of a two digit number is 12 if the digits are reversed the new number becomes 4/7 time the original number find the original number

Answer 1

Hi there!

Sum of digits $= x + y = 12 \\ y = 12 - x$

Two digit no. $= 10x + y \\ = 10x + 12 - x \\ = 9x + 12$

Reverse number $= 10y + x \\ = 10(12 - x) + x \\ = 120 - 10x + x \\ = 120 - 9x$

$ReverseNumber = \frac{4}{7}(OriginalNumber)$

$120 - 9x = \frac{4}{7}(9x + 12) \\ 120 - 9x = \frac{36x}{7} + \frac{48}{7} \\ 120 - 9x = \frac{36x+48}{7} \\ 7(120 - 9x) = 36x + 48 \\ 840 - 63x = 36x + 48 \\ 840 - 48 = 36x + 63x \\ 792 = 99x \\ x = 792/99 \\ x = 8$

$y = 12 - x \\ y = 12 - 8 \\ y = 4$

Original Number = $10x + y \\ 10(8) + 4 \\ 80 + 4 = 84$

Hope you found my answer useful.