Seven times a two digit number is equal to four times the number obtained by reversing the order of its digits. If the difference of the digits is 3, determine the number.

A 2-digit number can be represented by 10x + y.

So, let the number be 10x + y.

⇒ the number obtained on reversing the order of the digit = 10y + x

According to the question, seven times a two-digit number is equal to four times the number obtained by reversing the digit.

⇒ 7(10x + y) = 4(10y + x)

⇒ 70x + 7y = 40y + 4x

⇒ 70x – 4x = 40y – 7y

⇒ 66x = 33y

⇒ 2x = y …(i)

Also, digit if the digits is 3, y>x.

⇒ y – x = 3 …(ii)

Substituting equation (i) in equation (ii), we get

2x – x = 3

⇒ x = 3

Now putting x = 3 back in equation (i), we have

y =2(3) = 6

Since, the number was 10x + y, put x = 3 and y = 6 in it.

10(3) + 6 = 30 + 6 = 36

Hence, the number is 36.