Question 73

The ratio of the square of a number to the reciprocal of its cube is $$\frac{243}{16807}$$. What is the number

Solution

Let the number be $$\frac{x}{y}$$

Square of the number = $$\frac{x^{2}}{y^{2}}$$

Reciprocal of its cube = $$\frac{y^{3}}{x^{3}}$$

According to the question,

$$\frac{x^{2}}{y^{2}}\times\frac{x^{3}}{y^{3}}$$ = $$\frac{243}{16807}$$

$$\frac{x^{5}}{y^{5}}$$ = $$\frac{243}{16807}$$ = $$\frac{3^{5}}{7^{5}}$$

$$\frac{x}{y}$$ = $$\frac{3}{7}$$

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