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Question 54
The difference of the cubes of the two numbers is 999. The numbers are in the ratio of 4 : 3. What is the square of the smaller number?
Solution
The numbers are in the ratio of 4 : 3.
Let's assume the numbers are 4y and 3y respectively.
The difference of the cubes of the two numbers is 999.
$$\left(4y\right)^3-\left(3y\right)^3\ =\ 999$$
$$64y^3-27y^3\ =\ 999$$
$$37y^3\ =\ 999$$
$$y^3 =Â 27$$
$$y^3 = 3^3$$
y = 3
smaller number = 3y
= $$3\times3$$
= 9
Square of the smaller number =Â $$9^2$$
= 81
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