# Find two numbers whose sum is 27 and product is 182.

**Solution:**

Let us consider one of the numbers to be x. Then the other number will be 27 - x.

The product of the two numbers is given as 182

This can be written in the form of the following quadratic equation:

x(27 - x) = 182

x(27 - x) = 182

27x - x^{2} = 182

27x - x^{2} - 182 = 0

x^{2} - 27 x + 182 = 0 [Rearranging the terms and multiplying both sides by negative sign]

x^{2} - 14x - 13x + 182 = 0

x (x - 14) - 13 (x - 14) = 0

(x -13) (x - 14) = 0

x - 13 = 0 and x - 14 = 0

x = 13 and x = 14

Therefore, the required numbers are 13, 14.

**Video Solution:**

## Find two numbers whose sum is 27 and product is 182.

### Class 10 Maths NCERT Solutions - Chapter 4 Exercise 4.2 Question 3:

**Summary:**

Two numbers whose sum is 27 and product is 182 are 13 and 14.