Question

Question 134

Solve the following question:

Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

Answer 1

Let the numbers be 2x, 3x and 4x, respectively.
$\because$ Sum of their cubes = 0.334125 [given]
According to the question,
$(2x{)}^3+(3x{)}^3+(4x{)}^3=0.334125\Rightarrow 8x^3+27x^3+64x^3=0.334125\Rightarrow 99x^3=0.334125\Rightarrow x^3=\frac{0.334125}{99}\Rightarrow x^3=0.003375\Rightarrow x^3=\frac{3375}{1000000}$
$\Rightarrow x=\sqrt[3]{3\frac{15\times 15\times 15}{10\times 10\times 10\times 10\times 10\times 10}}$ [taking cube root on both sides]
$\Rightarrow x=\frac{15}{10\times 10}\therefore x=0.15$
Hence, the required numbers are $2\times 0.15$ , $3\times 0.15$ and $4\times 0.15$ i.e. 0.3, 0.45 and 0.6 .