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 reversed. Find the number.

Answer 1

Let the one’s digit be ‘a’ and ten’s digit be ‘b’

Then, the number is = 10b + a

Given, the number is 3 more than 4 times the sum of its digits.

⇒ 10b + a = 4(a + b) + 3

⇒ 10b + a = 4a + 4b + 3

⇒ 3a = 6b - 3

⇒ a = 2b - 1 -----(1)

Also, if 18 is added to the number, the digits are reversed.

⇒ 10b + a + 18 = 10a + b

⇒ 9a - 9b = 18

⇒ a – b = 2 using (1)

⇒ 2b - 1 - b = 

⇒ b = 3

Thus, again from (1)

a = 6 – 1 = 5

Hence, Number is 35.