Correct Answer - Option 3 : 35 and 40
Given:
The units digit of a 2-digit number exceeds the tens digit by 3
The product of the given number and the sum of its digits = 324
Concept Used:
Principle of Place Values (Units digit and Ten's Digit) of a number
Calculation:
Let the 2 digit number be (10x + y)
From the given conditions, we get the following equations:
y – x = 3 ----(i)
(10x + y) × (x + y) = 324 ----(ii)
From the equation (i), we get:
y = x + 3 ----(iii)
On substituting the value of equation (iii) into equation (ii), we get:
(10x + x + 3) × (x + x + 3) = 324
⇒ (11x + 3) × (2x + 3) = 324
⇒ 22x2 + 33x + 6x + 9 = 324
⇒ 22x2 + 39x – 315 = 0
⇒ [x + (105/22)](x – 3) = 0
As we cannot have a negative value of x,
⇒ x = 3 ----(iv)
Also, from equation (iii), we get:
y = 3 + 3 = 6 ----(v)
On combining equations (iv) and (v), we obtain the 2-digit number as:
(10 × 3) + 6 = 36
∴ The given two-digit number lies between 35 and 40