Property 1
The comparison of two scalar magnitudes of the same kinds is known as ratio. Ratio of a to b is denoted by
\(\samefrac{a}{b}\)
\(\samefrac{a}{b}=k\rightarrow\text{proportionality constant}\)
- \(\samefrac{a}{b}=\samefrac{3}{5}\Rightarrow \begin{aligned}a=3k\\b=5k\end{aligned}\)
- \(\samefrac{a}{3}=\samefrac{b}{5}\Rightarrow \begin{aligned}a=3k\\b=5k\end{aligned}\)
- \(\samefrac{a}{2}=\samefrac{b}{3}=\samefrac{c}{4}\Rightarrow \begin{aligned}a=2k\\b=3k\\c=4k\end{aligned}\)
- \((a:b:c)=(2:3:4)\Rightarrow \samefrac{a}{2}=\samefrac{b}{3}=\samefrac{c}{4}\)
1.
\(\samefrac{x}{y}=\samefrac{2}{3}\)
\(x+y=20\)
\(\Rightarrow x=?\)
2.
\(\samefrac{x}{y}=\samefrac{1}{3}\)
\(y-x=6\)
\(\Rightarrow x=?\)
3.
\(\samefrac{x}{3}=\samefrac{y}{5}\)
\(x+y=16\)
\(\Rightarrow x\cdot y=?\)
4.
\(\samefrac{x}{3}=\samefrac{y}{4}=\samefrac{z}{5}\)
\(x+y-z=8\)
\(\Rightarrow x\cdot y=?\)
5.
\(\samefrac{2}{x}=\samefrac{3}{y}=\samefrac{4}{z}\)
\(2x+y-z=3\)
\(\Rightarrow x\cdot y\cdot z=?\)
6.
\((a:b)=(2:3)\)
\(2a+b=14\)
\(\Rightarrow a\cdot b=?\)
7.
\((a:b:c)=(2:3:5)\)
\(\Rightarrow \samefrac{a+b}{c}=?\)
8.
\((a:b:c)=(3:4:5)\)
\(2a+b+c=45\)
\(\Rightarrow a=?\)
9.
\((a:b:c)=(2:3:4)\)
\(a-b+c=3\)
\(\Rightarrow a=?\)