Question

The sur two digit number and the number
formed by inter changing the digit is 130. sf 12 is
added to the number
the number, the new number
becomes 5 times the sum
of the digits find the
number​

Answer 1

Step-by-step explanation:

Correct Question:-

The sum of a two digit number and the number obtained by reversing the order of digits is 132. If 12 is added to the number ,new number becomes 5 times the sum of the digits of the original number. Find the number.

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

Let the tens digit of the number be x

And units digit of the number be y

Then:-

The original number = 10x + y

The number obtained by interchanging the digits = 10y + x

Case 1:-

The sum of a two digit number and the number obtained by reversing the order of digits is 132.

$\rm \implies (10x + y)+ (10y + x) = 132$

$\rm \implies 10x + x+ 10y + y= 132$

$\rm \implies 11x + 11y = 132$

Dividing the whole equation by 11

$\rm\implies x + y = 12......(i)$

Case 2:-

If 12 is added to the number ,new number becomes 5 times the sum of the digits of the original number.

$\rm\implies 10x + y + 12 = 5(x + y)$

$\rm\implies 10x + y + 12 = 5x + 5y$

$\rm\implies 10x + y - 5x - 5y = - 12$

$\rm\implies 5x - 4y = -12.....(ii)$

Multiplying equation (i) with 4

$\rm\implies 4(x + y = 12)$

$\rm\implies 4x + 4y = 48.....(iii)$

Adding equations (ii) from (iii)

$\rm\implies 4x + 4y + 5x - 4y = 48+ (-12)$

$\rm\implies 4x + 5x + 4y - 4y = 48 - 12$

$\rm\implies 9x = 36$

$\rm\implies x = 4$

Substituting x = 4 in equation (i)

$\rm\implies x + y = 12$

$\rm\implies 4 + y = 12$

$\rm\implies y = 12 - 4$

$\rm\implies y = 8$

We have:-

• x = 4

• y = 8

The original number = 10x + y

= 10(4) + 8

= 40 + 8

= 48

$\underline{\boxed{\purple{\rm \therefore The \: original \: number = 48}}}$