# The ratio of the sum, difference and product of two numbers is 11 : 1 : 120. What is the sum of their squares?

59 views

closed
The ratio of the sum, difference and product of two numbers is 11 : 1 : 120. What is the sum of their squares?
1. 549
2. 808
3. 656
4. 976

by (117k points)
selected

Correct Answer - Option 4 : 976

Given:

The ratio of the sum, difference, and product of two numbers is 11: 1: 120.

Calculation:

Let the two numbers be a and b, and the value of sum is 11x, the difference is 1x and the product is 120x. Now apply the above-given things.

⇒ a + b = 11x      ----(1)         and a × b = 120x      ----(3)

a - b = 1x       ----(2)     (Now add (1) & (2))

⇒ a = 6x and by putting in any equations we get b = 5x

Now put these values of a and b in equation (3)

⇒ 6x × 5x = 120x

⇒ x = 4

As x is 4, than the value of a and b will be

a = 6×4 = 24, b = 5×4 = 20

Now the squares of these two numbers a and b is

242 = 576, 202 = 400, Their sum is

a2 + b2 = 576 + 400 = 976

∴ The sum of the square of 2 numbers is 976