Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3, find the number.

Let digit at ten's place be x and digit at unit's place be y.

Number = 10(x) + y = 10x + y

On reversing the digits,

Reversed number = 10(y) + x = 10y + x

Given,

Seven times a two digit number is equal to four times the number obtained by reversing the digits.

⇒ 7(10x + y) = 4(10y + x)

⇒ 70x + 7y = 40y + 4x

⇒ 40y - 7y = 70x - 4x

⇒ 33y = 66x

⇒ y = $\dfrac{66x}{33}$

⇒ y = 2x ……….(1)

Given,

Difference between the digits is 3.

Let x > y

⇒ x - y = 3 ……….(2)

Let y > x

⇒ y - x = 3 ……….(3)

Substituting value of y from equation (1) in equation (2), we get :

⇒ x - 2x = 3

⇒ -x = 3

⇒ x = -3

This is not possible as digits cannot be negative.

Substituting value of y from equation (1) in equation (3), we get :

⇒ 2x - x = 3

⇒ x = 3

Substituting value of x in equation (1), we get :

⇒ y = 2x = 2(3) = 6.

Number = 10x + y = 10(3) + 6 = 30 + 6 = 36.

Hence, number = 36.