Question
Determine if the following ratios form a proportion. Also, write the middle forms and extreme terms where the ratios form a proportion. $25\ cm : 1m$ and $₹40 : ₹160.$
✓
Answer
$\because$ $1m = 100\ cm$
$\therefore$ $25\ cm : 1m = 25\ cm : 100\ cm$
$=\frac{25}{100}=\frac{25 \div 25}{100 \div 25}$ $[$$\therefore$$H.C.F.(25, 100) = 25]$
$=\frac{1}{4}$ $= 1 : 4$
$₹40 : ₹160$$=\frac{40}{160}=\frac{40 \div 40}{160 \div 40}$ $[$$\therefore$$H.C.F.(40, 160) = 40]$
$=\frac{1}{4}$ $= 1 : 4$
Since the two ratios are equal, therefore, the given ratios are in proportion. Middle terms are $1m$ and $₹40.$
Extreme terms are $25 \ cm$ and $₹160.$
$\therefore$ $25\ cm : 1m = 25\ cm : 100\ cm$
$=\frac{25}{100}=\frac{25 \div 25}{100 \div 25}$ $[$$\therefore$$H.C.F.(25, 100) = 25]$
$=\frac{1}{4}$ $= 1 : 4$
$₹40 : ₹160$$=\frac{40}{160}=\frac{40 \div 40}{160 \div 40}$ $[$$\therefore$$H.C.F.(40, 160) = 40]$
$=\frac{1}{4}$ $= 1 : 4$
Since the two ratios are equal, therefore, the given ratios are in proportion. Middle terms are $1m$ and $₹40.$
Extreme terms are $25 \ cm$ and $₹160.$
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