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 tens and the units digits of the required number be x and y, respectively.

Required number = (10x + y)

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

⇒10x + y = 4x + 4y + 3

⇒ 6x – 3y = 3

⇒ 2x – y = 1   ...(i)

Again, we have:

10x + y + 18 = 10y + x

⇒ 9x – 9y = –18

⇒ x – y = –2   ...(ii)

On subtracting (ii) from (i), we get:

x = 3

On substituting x = 3 in (i) we get

2 × 3 – y = 1

⇒ y = 6 – 1

⇒ y = 5

Required number = (10x + y)

= 10 × 3 + 5

= 30 + 5

= 35

Hence, the required number is 35.