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 = 5
Required number = (10x + y) = 10 × 3 + 5 = 30 + 5 = 35
Hence, the required number is 35.