The sum of the cubes of two numbers in the ratio 3 : 4 is 5824. The sum of the numbers is :

A. $${\left( {5824} \right)^{\frac{1}{3}}}$$

B. 28

C. 24

D. 14

Answer: Option B

Solution(By Examveda Team)

Let numbers are = 3x, 4x
(3x)³ + (4x)³ = 5824
27x³ + 64x³ = 5824
91x³ = 5824
x³ = $$\frac{5824}{91}$$
x³ = 64
x = 4
So, numbers are
3x = 3 × 4 = 12
4x = 4 × 4 = 16
Sum = 12 + 16 = 28