If the sum of two natural numbers is 27 and their product is 182, then the smaller number is :

1. 13

2. 14

3. 16

4. 18

Let two natural numbers be x and y.

Given,

Sum of numbers = 27

⇒ x + y = 27

⇒ y = 27 - x     ………(1)

Given,

Product of numbers is 182.

⇒ xy = 182     ………(2)

Substituting value of y from equation (1) in equation (2), we get :

⇒ x(27 - x) = 182

⇒ 27x - x² = 182

⇒ x² - 27x + 182 = 0

⇒ x² - 13x - 14x + 182 = 0

⇒ x(x - 13) - 14(x - 13) = 0

⇒ (x - 14)(x - 13) = 0

⇒ (x - 14) = 0 or (x - 13) = 0     [Using zero-product rule]

⇒ x = 14 or x = 13.

Substituting value of x in equation (1), we get :

If x = 14, y = 27 − 14 = 13

If x = 13, y = 27 − 13 = 14.

The smallest number among two numbers is 13.

Hence, option 1 is the correct option.