Question

If the difference between two numbers is 6 and the difference between their squares is 60, what is the sum of their cubes ?
1. 894
2. 945
3. 678
4. 520

Answer 1

Correct Answer - Option 4 : 520

Given: 

The difference between 2 numbers = 6 

Formula Used:

a² - b² = (a - b)(a + b) 

Calculation: 

Let two number be a and b respectively [Where a > b]

Accordingly, 

a - b = 6      ----(1)

And,

a2 - b² = 60

⇒ 60 = (a + b)(a - b)

⇒ 60 = 6(a + b) 

⇒ (a + b) = 10      ----(2)

From (1) and (2) get,

a = 8, b = 2 

Sum of their cube = a³ + b³ = 8³ + 2³ = 512 + 8 = 520 

∴ The sum of their cube is 520.