Question

In a two - digit number, the unit's digit exceeds its ten's digit by 4. If the product of the given number and the sum of its digits is 370, then what is the number?
1. 62
2. 37
3. 26
4. 73

Answer 1

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.