Question

The sum of the digits of a 2-digit number is 11. If we add 45 to the number, the new number obtained is a number formed by the interchange of the digits. What is the number?

Answer 1

EXPLANATION.

Let the ten's place be = x

Let the unit place be = y

original number = 10x + y

reversing number = 10y + x

Case = 1.

The sum of digit of a two digit number is = 11

=> x + y = 11 ...... (1)

Case = 2.

If 45 is added to the number the new number

obtained is a number formed by the

interchanging of its digit.

=> 10x + y + 45 = 10y + x

=> 9x - 9y = -45

=> x - y = -5 ..... (2)

From equation (1) and (2) we get,

=> 2x = 6

=> x = 3

put the value of x = 3 in equation (1)

we get,

=> 3 + y = 11

=> y = 8

Therefore,

original number = 10x + y

=> 10(3) + 8 = 38

original number = 38

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The sum of digits of a two digits number is 11.

• Is we add 45 to the number, the new number obtained is formed by the interchange of the digits.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The number.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the tens digit of the number be x

And ones digit be y

The original number = 10x + y

The revered number = 10y + x

According to the 1st condition:-

The sum of the digits of a number is 11.

$\implies \rm x + y = 11.....(i)$

According to the 2nd condition:-

If we add 45 to the number, the new number obtained is a number formed by the interchange of the digits.

$\implies \rm (10x + y ) + 45= 10y +x$

$\implies \rm 10x + y + 45= 10y +x$

$\implies \rm 10x - x+ y - 10y = - 45$

$\implies \rm 9x - 9y = - 45$

Dividing whole equation by 9

$\implies \rm x - y = - 5....(ii)$

Adding equation (i) and (ii)

$\rm x + \not y = 11$

$\rm x - \not y = - 5$

_______________

$\rm\implies 2x = 11 - 5$

$\rm \implies 2x = 6$

$\rm \implies x= 3$

Substituting x = 3 in equation (i)

$\rm \implies x + y = 11$

$\rm \implies 3+ y = 11$

$\rm \implies y = 11 - 3$

$\rm \implies y = 8$

We have x = 3 and y = 8

The original number

= 10x + y

= 10(3) + 8

= 30 + 8

= 38.

$\boxed{\rm \therefore The \: number \: is \: 3 8}$