Question
Determine if the ratio form a proportion. Also, write the middle term and extreme term where the ratio form a proportion:
$200\ ml:$ $2.5$ litre and $₹4 : ₹50.$
$200\ ml:$ $2.5$ litre and $₹4 : ₹50.$
✓
Answer
$2.5\ litre = 2.5$ $\times$ $1000\ ml = 2500\ ml$
$\therefore$ $200\ ml : 2.5\ litre = 200\ ml : 2500\ ml$
$=\frac{200}{2500}=\frac{200 \div 100}{2500 \div 100}$ $[$$\therefore$$H.C.F.(200, 2500) = 100]$
$=\frac{2}{25}$ $= 2 : 25$
$₹4 : ₹ 50$ $=\frac{4}{50}=\frac{4 \div 2}{50 \div 2}$ $[$$\therefore$$H.C.F.(4, 50) = 2]$
$=\frac{2}{25}$ $= 2 : 25$
Since the two ratios are equal, therefore, the given ratios are in proportion.
Middle terms are $2.5$ $litres$ and $₹4$.
Extreme terms are $200\ ml$ and $₹50.$
$\therefore$ $200\ ml : 2.5\ litre = 200\ ml : 2500\ ml$
$=\frac{200}{2500}=\frac{200 \div 100}{2500 \div 100}$ $[$$\therefore$$H.C.F.(200, 2500) = 100]$
$=\frac{2}{25}$ $= 2 : 25$
$₹4 : ₹ 50$ $=\frac{4}{50}=\frac{4 \div 2}{50 \div 2}$ $[$$\therefore$$H.C.F.(4, 50) = 2]$
$=\frac{2}{25}$ $= 2 : 25$
Since the two ratios are equal, therefore, the given ratios are in proportion.
Middle terms are $2.5$ $litres$ and $₹4$.
Extreme terms are $200\ ml$ and $₹50.$
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