Question

If product of two numbers be 32. If the average of these numbers is 6, then sum of the cube of these numbers will be
1. 864
2. 576
3. 624
4. 430

Answer 1

Correct Answer - Option 2 : 576

Given:

Product of two numbers = 32

Average of numbers = 6

Formula Used:

Average = Sum of all items / Number of items 

Calculation:

Let assume that the first number is x

And the second number is y

According to the question:

x × y = 32                              ........................(1)

(x + y)/2 = 6

⇒ x + y =12                         

⇒ x = 12 - y   ..........................(2)

From equation (1) and (2)

(12 - y) × y = 32

⇒ 12y - y² = 32

⇒ y² - 12y + 32 = 0

⇒ y² - 8y - 4y +32 = 0

⇒ (y - 8)(y - 4) = 0

y - 8 = 0

⇒ y = 8

y - 4 = 0

⇒ y = 4

If y = 8, Then x = 4

If y = 4, Then x = 8

⇒ (8)³ + (4)³ = 576

∴ The sum of cube of these number will be 576. 

The correct option is 2 i.e. 576