Question

4 Determine the following rates from a proto
- Also, write the middle term and extre
terms where the ratio from a proportion 25cm:1m:: rupees 40: rupees 160​

Answer 1

Answer:

Here, 25 cm : 1 m = 25 cm : 1 \times 100 cm                 [\because 1 m = 100 cm] =25:100=\frac{25}{100}=\frac{25\div 25}{100\div 25}=\frac{1}{4}=1:4 [dividing numerator and denominator both by 25] and Rs. 40 : Rs. 160 = 40 : 160 =\frac{40}{160}=\frac{4}{16}=\frac{1}{4}=1:4 [dividing numerator and denominator both by 10] Here, 1 : 4 = 1 : 4 i.e. 25 cm : 1 m = Rs. 40 : Rs. 160 So, the ratios of 25 cm : 1 m and Rs. 40 : Rs. 160 are in proportion. i.e. 25 cm : 1 m :: Rs. 40 : Rs. 160 Now, middle terms are 1 m and Rs. 40 and extreme terms are 25 cm and Rs. 160. (b) Here,39L:65L=39:65=\frac{39}{65}=\frac{39\div 13}{65\div 13}      [\because HCF of 39 and 65 = 13] =\frac{3}{5}=3:5 and 6 bottles : 10 bottles =6:10=\frac{6}{10}=\frac{6\div 2}{10\div 2}=\frac{3}{5}=3:5 [dividing numerator and denominator both by 2] Here, 3 : 5 = 3 : 5 i.e. 39 L : 65 L = 6 bottles : 10 bottles So, the ratio of 39 L : 65 L and 6 bottles : 10 bottles are in proportion. i.e. 39 L : 65 L : : 6 bottles : 10 bottles. Now, middle terms of ratios are 65 L and 6 bottles and extreme terms of ratios are 39 L and 10 bottles. (c) Here,  2kg:80kg=2:80=\frac{2}{80}=\frac{2\div 2}{80\div 2}=\frac{1}{40}=1:40 [dividing numerator and denominator both by 2] and25g:625g=25:625=\frac{25}{625}=\frac{25\div 25}{625\div 25}=\frac{1}{25}=1:25[\because HCF of 25 and 625=5\times 5=25] Since, both ratios are not equal. \therefore   \text{2 kg : 80 kg }\ne \text{ 25 g : 625 g } Hence, the given ratios are not in proportion. (d) Here, 200mL:2.5L=200\times \frac{1}{1000}L:2.5L \left[ \because 1mL=\frac{1}{1000}L \right] =\frac{200}{1000}L:2.5L=0.200L:2.5L =0.200:2.5=\frac{0.200}{2.5}=\frac{2}{25}=2:25 [multiplying numerator and denominator both by 10] and  Rs. 4 : Rs. 50 = 4 : 50 =\frac{4}{50}=\frac{4\div 2}{50\div 2}=\frac{2}{25}=2:25 [dividing numerator and denominator both by 2] Here, 2 : 25 = 2 : 25 i.e. 200 mL : 2.5 L = Rs. 4 : Rs. 50 So, the ratios of 200 mL : 2.5 L and Rs. 4 : Rs. 50 are in proportion. i.e. 200 mL : 2.5 L : : Rs. 4 : Rs. 50 Now, middle terms of ratios are 2.5 L and Rs. 4 and extreme terms of ratios are 200 mL and Rs. 50.

Step-by-step explanation: