Question

the sum of the digits of a two digit number is 10. the number formed by interchanging the digits is 36 less than the original number. find the original number [ USING LINEAR EQUATIONS IN ONE VARIABLE]

Answer 1

$\sf{\underbrace{Answer\implies 73}}$

$\sf\large\underline{Let:}$

$\sf{\implies The\:ones\:digit=y}$

$\sf{\implies The\:tens\:digit=x}$

$\sf{\implies The\: orginal\:number=10x+y}$

$\sf{\implies The\: reversed\:number=10y+x}$

$\sf\large\underline{To\: Find}$

$\sf{\implies The\: orginal\:number=?}$

$\sf\large\underline{Solution:}$

$\sf\small\underline{Given\:here:}$

• the sum of the digits of a two digit number is 10. the number formed by interchanging the digits is 36 less than the original number]

$\tt{\implies x+y=10---(i)}$

• Given difference between orginal number and reverse number is 36]

$\tt{\implies (10x+y)-(10y+x)=36}$

$\tt{\implies 10x+y-10y-x=36}$

$\tt{\implies 9x-9y=36}$

• Here dividing by 9 on both sides]

$\tt{\implies x-y=4-----(ii)}$

• Now add eq (i) and (ii) here]

$\tt{\implies x+y=10}$

$\tt{\implies x-y=4}$

• By solving we get here]

$\tt{\implies 2x=14=>x=7}$

• Putting the value of x=7 in eq (i)]

$\tt{\implies x+y=10}$

$\tt{\implies 7+y=10}$

$\tt{\implies y=10-7=>y=3}$

Hence,

The original number=10x+y=>10×7+3=>73

$\sf{\implies Something\:to\:know\: about\:it}$

As given in Question we have to solve this question in one variable. It is not possible to solve in one variable because in the question two different conditions is given so we have to assume 2 different variable.

Answer 2

Let assume ones and ten's digit are x and y respectively

Given

sum of 2 digit number=10

x+y=100

the number formed by interchanging the digits is 36 less than the original number

10x+y-36=10y+x

x-y=4

if we solve equation 1 and 2 we get

• X=7 y=3

therefore orginal number=10x+y

=>10×7+3=73