Question

A two digit number is 3 more than 4 times
the sum of its digits. If 18 is added to
the number, the digits are revered. Find the
number.​

Answer 1

Let the Tens digit of the number be x

One's digit be y

Original Number = (10x + y)

On reversing → (10y + x)

According to the question,

10x + y = 4(x + y) + 3

⇒ 10x + y = 4x + 4y + 3

⇒ 10x - 4x = 4y - y + 3

⇒ 6x = 3y + 3

⇒ 3y + 3 = 6x

⇒ 3(y + 1) = 6x

⇒ y + 1 = 2x

⇒2x - y = 1 ----- (Equation 1)

Also,

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

10x + y + 18 = 10y + x

⇒10x - x + 18 = 10y - y

⇒ 9x + 18 = 9y

⇒ 9(x + 2) = 9y

⇒ x + 2 = y

⇒ x - y = -2 ----- (Equation 2)

Subtracting Equation 1 and Equation 2,

2x - y = 1

(-) x - y = -2

x = 1 + 2

∴ x = 3

Substitute value of x in Any one of the equation.

Here, let us substitute in Equation 2

x - y = -2

3 - y = -2

⇒y = 5

We know that original number is of the form

(10x + y)

= 10(3) + 5

= 30 + 5

= 35

So the required number is 35