Correct Answer - Option 2 : 37
Given:
The unit's digit exceeds its ten's digit by 4.
The product of the given number and the sum of its digits is 370.
Concept Used:
The number = 10x + y
Here, x = ten's place digit y = unit's place digit
Calculation:
The unit's digit exceeds its ten's digit by 4.
Let the unit's digit be y.
Let the ten's digit be x.
The number = 10x + y
According to the question;
The unit's digit exceeds its ten's digit by 4.
⇒ y = x + 4
The product of the given number and the sum of its digits is 370.
⇒ (10x + y) × (x + y) = 370
⇒ (10x + x + 4) × (x + x + 4) = 370
⇒ (11x + 4) × (2x + 4) = 370
⇒ 22x2 + 44x + 8x + 16 = 370
⇒ 22x2 + 52x + 16 = 370
⇒ 22x2 + 52x - 354 = 0
⇒ 11x2 + 26x - 177 = 0
⇒ x = - 59/100, 33/11
⇒ x = - 59/100, 3
The ten's digit = 3
The unit's digit = 3 + 4 = 7
The number = 10x + y = 3 × 10 + 7 = 37
∴ The two digit number is 37.