The difference of cubes of two numbers is 999. The numbers are in the ratio of 4 : 3. What is the square of the smaller number?

49 81 64 100

81

⇒ \( {4x }^{3 } \) - \( {3x }^{3 } \) = 999 ⇒ \( {64x }^{3 } \) - \( {27x }^{3 } \) = 999 ⇒ \( {37x }^{3 } \) = 999 ⇒ \( {x }^{3 } \) = 27 ⇒ x = \(\sqrt[3]{27 }\) ⇒ x = 3, ⇒ Square of smaller number = 3 x 3 = 9 x 9 = 81.