Question

9. A two-digit number is 3 more than 4 times the sum of its digt. If 18 is added to the digits the
diguts are reversed. Find the number​

Answer 1

Step-by-step explanation:

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

• A two-digit number is 3 more than 4 times the sum of its digits.

• If 18 is added to the digits the digits are reversed.

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

• The original number.

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

Let the tens digit of the number be x

And ones digit of the number be y

The sum of digits = x + y

The original number = 10x + y

The reversed number = 10y + x

According to the 1st condition:-

A two-digit number is 3 more than 4 times the sum of its digits.

$\rm \implies10x + y = 4(x + y) + 3$

$\rm \implies10x + y = 4x + 4y + 3$

$\rm \implies10x + y - 4x - 4y = 3$

$\rm \implies6x - 3y = 3$

Dividing whole equation by 3

$\rm \implies2x - y = 1.....(i)$

According to the 2nd condition:-

If 18 is added to the digits the digits are reversed.

$\rm \implies18 + original \: number = reversed \: number$

$\rm \implies18 +10x + y = 10y + x$

$\rm \implies 10x + y - 10y - x = - 18$

$\rm \implies 9x - 9y= - 18$

Dividing the whole equation by 9

$\rm \implies x - y= - 2......(ii)$

Subtracting equation (ii) from (i)

$\rm \implies 2x -y - (x - y)= 1 - ( - 2)$

$\rm \implies 2x -y - x + y= 1 + 2$

$\rm \implies x = 3$

Substituting x = 3 in equation (i)

$\rm \implies 2x - y = 1$

$\rm \implies 2(3) - y = 1$

$\rm \implies6- y = 1$

$\rm \implies- y = 1 - 6$

$\rm \implies- y = - 5$

$\rm \implies y = 5$

The original number:-

= 10x + y

= 10(3) + 5

= 30 + 5

= 35

$\large\underline{ \boxed{ \purple{\bf \therefore The \: number =35}}}$