Question

the sum of the digits of a two digit number is 7. the number is 2 more than twice the number formed by interchanging the digit of the number.find the number

Answer 1

let first number unit place is equal to X and second tens place is equal to Y then the number will be 10 Y + x according to question the sum of two digit number is equal to 7 then X + Y is equal to 7 equation 1. 10 Y + x is equal to 2 (10 X + Y) plus 2




$10y + x = 20x + 2y + 2$
$x - 20x + 10y - 2y = 2$
$- 19x + 8y = 2$
By substituting method.
$x + y = 7$
$- 19x + 8y = 2$
then cross multiply 8 by equation
1 and 1 by question 2.

$8x + 8y = 56$
$- 19x + 8y = 2$
$+ - = -$
$27x = 54$
$x = 54 \div 27$
$x = 2$




then put the value of x in equation 1

$x + y = 7$
$2 + y = 7$
$y = 7 - 2$
$y = 5$

then put the value of x y in equation
$10y + x$
$10(5) + (2)$
$50 + 2$
$52$