Question

Determine if the following ratios form a proportion. Also write the middle terms and extreme terms where the ratios form a proportion.
(i) $25cm:1$ m and $Rs.40:Rs.160$
(ii) $39$ litres : $65$ litres and $6$ bottles $:10$ bottles
(iii) $2kg:80kg$ and $25g:625g$
(iv) $200mL:2.5L$ and $Rs.4:Rs.50$

Answer 1

(i) $25cm:1m$ and $Rs.40:Rs160$ or, $25cm:100cm$ and $Rs.40:Rs.160$

$\frac{25cm}{100cm}=\frac{25÷25}{100÷25}=\frac{1}{4}$

$\frac{Rs.40}{Rs.160}=\frac{40÷40}{160÷40}=\frac{1}{4}$

so, both ratios are equal. hence they are in proportion.

Middle terms $=1m$ and $Rs.40$

Extremes terms $=25cm$ and $Rs.160$

(ii) $39$ litres $:65$ litres and $6$ bottles $:10$ bottles

$\frac{\text{39~litres}}{\text{65~litres}}=\frac{39÷13}{65÷13}=\frac{3}{5}$

$\frac{\text{3~bottles}}{\text{10~bottles}}=\frac{3÷2}{10÷2}=\frac{3}{5}$

so, both ratios are equal. hence they are in proportion.

Middle terms $=65$ litres and $6$ bottles

Extremes terms $=39$ litres and $10$ bottles

(iii) $200mL:2.5L$ and $Rs.4:Rs.50$ or, $200mL:2500mL$ and $Rs.4:Rs.50$

$\frac{200ml}{2500ml}=\frac{200÷100}{2500÷100}=\frac{2}{25}$

$\frac{Rs.4}{Rs.50}=\frac{4÷2}{50÷2}=\frac{2}{25}$

so, both ratios are equal. hence they are in proportion.

Middle terms $=2.5L$ and $Rs.4$

Extremes terms $=200mL$ and $Rs.50$

(iv) $2kg:80kg$ and $25g:625g$ or, $2kg:80kg$ and $25g:625g$

$\frac{2kg}{80kg}=\frac{2÷2}{80÷2}=\frac{1}{40}$

$\frac{25g}{625g}=\frac{25÷25}{625÷25}=\frac{1}{25}$

So, in this case the ratios are not equal.Hence, they are not in proportion.