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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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