Question

Sum of the digits of a two digit number is 17. If 72 is added to the original number the digits interchange their places. Write two linear equation representing these situations.

Answer 1

Answer:

2nd equation x-y+8=0......

Answer 2

$Let \: Ten's \:place \: digit = x$

$and \: Unit \: place \:digit = y$

$\blue { Original \: number } = 10x + y$

/* According to the problem given */

$Sum \:of \:the \:digits = 17$

$\implies \pink { x + y = 17 } \: ---(1)$

$and \: Original \:number + 72$

$= Interchange \:the \:digits \: of \: original \:number$

$\implies 10x+y + 72 = 10y + x$

$\implies 10x - x + y - 10y = -72$

$\implies 9x - 9y = -72$

/* Dividing each term by 9, we get */

$\implies\green { x - y = - 8 }\: ---(2)$

Therefore.,

$\red{ Required \: two \:linear \: equations : }$

$\pink { x + y = 17 } \: ---(1)$

$\green { x - y = - 8 }\: ---(2)$

•••♪