Question

Two numbers are in ratio 4:5. If the difference of their cubes is 61 , find the numbers.

Answer 1

let the numbers are 4x and 5x

(5x)^3 - (4x)^3 = 61

125x^3 - 64x^3 = 61

61x^3 = 61

x^3 = 1

x = 1

The numbers are
4x = 4×1 = 4
5x = 5×1 = 5

Answer 2

Given, a:b = 4:5
=> b = 5/4 a
Now,
a³ - (5a/4)³ = 61
=>64a³ - 125a³ = 61 * 64
=> -61a³ = 61 * 64
=> a³ = -64
=> a = -4
Therefore, the no.s are -4,-5.....