Question

A two-digit number is such that the product of its digits is 35. If 18 is added to the number, the digits interchange their places. Find the number.

Answer 1

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

Then, we have: 

xy = 35 …….(i) 

Required number = (10x + y) 

Number obtained on reversing its digits = (10y + x) 

∴(10x + y) + 18 = 10y + x 

⇒9x – 9y = -18 

⇒ 9(y – x) = 18 

⇒ y – x = 2 ……..(ii)

We know: 

(y + x)² – (y – x)² = 4xy

⇒ y + x = 12 ……..(iii) (∵ x and y cannot be negative) 

On adding (ii) and (iii), we get: 

2y = 2 +12 = 14 

⇒y = 7 

On substituting y = 7in (ii) we get 

7 – x = 2 

⇒ x = (7 – 2) = 5 

∴ The number = (10x + y) = 10 × 5 + 7 = 50 + 7 = 57 

Hence, the required number is 57.