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?
Answer & explanation
Correct answer: option 2
⇒ \( {4x }^{3 } \) - \( {3x }^{3 } \) = 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.