Question

The sum of the digits of a two digit number is 7 . If the digits are reversed, the number is reduced by 27 .Find the number.


please help​

Answer 1

Step-by-step explanation:

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

• The sum of digits of a two digit number is 7

• If the digits are reversed, the number is reduced by 27.

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

• The original number.

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

Let the tens digit of the number be x

And units digit be y

Then:-

The original number = 10x + y

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

Case 1:-

The sum of digits of the number is 7

$\rm x + y = 7$

Case 2:-

If the digits are reversed, the number is reduced by 27.

$\rm Original \: number = Reversed \: number- 27$

$\rm\implies 10x + y = 10y + x - 27$

$\rm \implies 10x + y - (10y + x) = 27$

$\rm \implies 10x + y - 10y - x = 27$

$\rm \implies 9x- 9y = 27$

Dividing the whole equation by 9

$\rm \implies x - y = 3......(ii)$

Adding equations (i) and (ii)

$\rm \implies x + y + x - y = 7 + 3$

$\rm \implies 2x = 10$

$\rm \implies x= 5$

Substituting x = 5 in equation (i)

$\rm \implies x+ y = 7$

$\rm \implies 5 + y = 7$

$\rm \implies y = 2$

The original number = 10x + y

= 10(5) + 2

= 50 + 2

= 52

$\underline{\boxed{\purple{\rm \therefore The \: original \: number = 52}}}$