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Determine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) 25 cm : 1 m and Rs. 40 : Rs. 160
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
(c) 2 kg : 80 kg and 25 g : 625 g
(d) 200 ml : 2.5 litre and Rs.4 : Rs. 50.
To do:
We have to determine whether the given ratios form a proportion and also the middle terms and extreme terms where the ratios form a proportion.
Solution:
We know that,
The proportion is defined as the equality of two ratios.
If $p,q,r,s$ are in proportion then,
$\frac{p}{q} = \frac{r}{s}$.
(a) We know that,
$1\ m = 100\ cm$
Therefore,
We get,
$25\ cm : 100\ cm$ and $Rs. 40: Rs.160$
The ratio of $25\ cm: 100\ cm$
$=\frac{25\ cm}{100\ cm}$
$=\frac{1}{4}$
The ratio of $Rs. 40: Rs.160$
$=\frac{Rs. 40}{Rs. 160}$
$=\frac{1}{4}$
Therefore,
$25\ cm : 100\ cm = \frac{1}{4} = Rs. 40 : Rs.160$
$25\ cm : 1\ m$ and $Rs. 40: Rs.160$ are in proportion.
The middle terms are $1\ m$ and $Rs. 40$.
The extreme terms are $25\ cm$ and $Rs. 160$.
(b) The ratio of $39\ litres: 65\ litres$
$=\frac{39\ litres}{65\ litres}$
$=\frac{3}{5}$
The ratio of $6\ bottles: 10\ bottles$
$=\frac{6\ bottles}{10\ bottles}$
$=\frac{3}{5}$
Therefore,
$39\ liters : 65\ litres = \frac{3}{5} = 6\ bottles : 10\ bottles$
$39\ litres: 65\ litres$ and $6\ bottles: 10\ bottles$ are in proportion.
The middle terms are $65\ litres$ and $6\ bottles$.
The extreme terms are $39\ litres$ and $10\ bottles$.
(c) The ratio of $2\ kg : 80\ kg$
$=\frac{2\ kg}{80\ kg}$
$=\frac{1}{40}$
The ratio of $25\ g: 625\ g$
$=\frac{25\ g}{625\ g}$
$=\frac{1}{25}$
Therefore,
$ \frac{1}{40} ≠ \frac{1}{25}$
$2\ kg : 80\ kg$ and $25\ g : 625\ g $ are not in proportion.
(d) We know that,
$1\ litre = 1000\ ml$
This implies,
$2.5\ litres = 2.5\times1000\ ml$
$2.5\ litres = 2500\ ml$
The ratio of $200\ ml: 2500\ ml$
$=\frac{200\ ml}{2500\ ml}$
$=\frac{2}{25}$
The ratio of $Rs.\ 4: Rs.\ 50$
$=\frac{Rs.\ 4 }{Rs.\ 50}$
$=\frac{2}{25}$
Therefore,
$200\ ml : 2500\ ml= \frac{2}{25} = Rs.\ 4 : Rs.\ 50$
$200\ ml : 2.5\ litres$ and $Rs. 4 : Rs. 50$ are in proportion.
The middle terms are $2.5\ litres$ and $Rs.\ 4$.
The extreme terms are $200\ ml$ and $Rs.\ 50$.
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