Question

Two numbers are respectively $20\%,50\%$ more than a third number. The ratio of the two numbers is _______ .

Answer 1

Calculating the numbers:

Consider the first, second, and third numbers to be$x,y,$ $z$ respectively.

The first number is given as $20\%$ more than the third number.

$$\begin{gathered} \Rightarrow \mathrm{x}=\mathrm{z}+\frac{20}{100}\mathrm{z} \\ \Rightarrow \mathrm{x}=\frac{100\mathrm{z}+20\mathrm{z}}{100} \\ \Rightarrow \mathrm{x}=\frac{120\mathrm{z}}{100} \\ \Rightarrow \mathrm{x}=\frac{6\mathrm{z}}{5} \end{gathered}$$

The second number is given as $50\%$ more than the third number.

$$\begin{gathered} \Rightarrow \mathrm{y}=\mathrm{z}+\frac{50}{100}\mathrm{z} \\ \Rightarrow \mathrm{y}=\frac{100\mathrm{z}+50\mathrm{z}}{100} \\ \Rightarrow \mathrm{y}=\frac{150\mathrm{z}}{100} \\ \Rightarrow \mathrm{y}=\frac{3\mathrm{z}}{2} \end{gathered}$$

Calculating the ratio of the first and second numbers:

The ratio of first and second numbers is $\mathrm{x}:\mathrm{y}$.

$$\begin{gathered} \mathrm{x}:\mathrm{y}=\frac{6\mathrm{z}}{5}:\frac{3\mathrm{z}}{2} \\ \Rightarrow \mathrm{x}:\mathrm{y}=12\mathrm{z}:15\mathrm{z} \\ \Rightarrow \mathrm{x}:\mathrm{y}=4:5 \end{gathered}$$

Therefore, the ratio of two numbers is $4:5$.