Final answer:
To determine if the ratios form a proportion, the fractions representing them are compared after converting to the same units if necessary. Ratios 25 cm : 1 m and ₹40 : ₹160; 39 liters : 65 liters and 6 bottles : 10 bottles; 2 kg : 80 kg and 25 g : 625 g form proportions after simplification. The ratio 200 mL : 2.5 liters and ₹4 : ₹50 does not form a proportion.
Step-by-step explanation:
To determine if the given ratios form a proportion, we need to compare the equivalent forms of the ratios. Two ratios form a proportion if their cross-products are equal. That is, if a/b = c/d, then a x d = b x c.
For the pair 25 cm : 1 m and ₹40 : ₹160, we must convert the meters into centimeters to compare the units uniformly. Since 1 meter is 100 centimeters, the ratio 25 cm : 1 m becomes 25 cm : 100 cm. Then, we can write the ratios as fractions and compare: 25/100 = 40/160. Simplifying 40/160 we get 1/4, which is equal to the simplified form of 25/100, hence this pair forms a proportion. The middle terms are 25 and 160, while the extreme terms are 100 and 40.
For 39 liters : 65 liters and 6 bottles : 10 bottles, we can directly compare the ratios as 39/65 = 6/10. When both ratios are simplified, they become 3/5, indicating that this pair forms a proportion as well. The middle terms are 39 and 10, and the extremes are 65 and 6.
For 2 kg : 80 kg and 25 g : 625 g, we must convert kilograms to grams since 1 kg = 1000 g. The ratios in grams are then: 2000 g : 80,000 g and 25 g : 625 g. We can compare these as 2000/80000 = 25/625. Simplified, both become 1/40, thus this pair forms a proportion. The middle terms are 2000 and 625, while the extreme terms are 80,000 and 25.
For 200 mL : 2.5 liters and ₹4 : ₹50, we must convert liters to milliliters, as 1 liter = 1000 milliliters. The ratio then becomes 200 mL : 2500 mL. Comparing the ratios: 200/2500 = 4/50. Simplified, these ratios are not equal (1/12.5 and 2/25 respectively), and thus they do not form a proportion.