The sum of two numbers is 20 and the difference between their squares is 80. Select the two numbers from the given options.

Correct option is D

Given:

Sum of two numbers = 20

Difference between their squares = 80

Concept Used:

Algebraic identities: a² - b² = (a + b)(a - b)

Solution:

Let the two numbers be 'a' and 'b'.

a + b = 20 .... (1)

a² - b² = 80

80 = (20)(a - b)

a - b = 4 .....(2)

Adding the two equations:

2a = 24

a = 12

Substituting the value of 'a' in the first equation:

12 + b = 20

b = 20 - 12

b = 8

The two numbers are 12 and 8.