Answer :
Sure! Let's check each statement to see if the ratios given on both sides are equal.
(a) 40 persons : 200 persons = ₹15 : ₹75
To determine if the ratios are equal, we can simplify each ratio:
- Simplify the ratio of persons:
[tex]\( \frac{40}{200} = \frac{1}{5} \)[/tex]
- Simplify the ratio of money:
[tex]\( \frac{15}{75} = \frac{1}{5} \)[/tex]
Since both simplified ratios are equal, the statement is true.
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
Let's simplify each ratio as well:
- Simplify the ratio of litres:
[tex]\( \frac{7.5}{15} = \frac{1}{2} \)[/tex]
- Simplify the ratio of kilograms:
[tex]\( \frac{5}{10} = \frac{1}{2} \)[/tex]
Both simplified ratios are equal, so this statement is true.
(c) 99 kg : 45 kg = ₹44 : ₹20
For this statement, simplify each:
- Simplify the ratio of kilograms:
[tex]\( \frac{99}{45} = \frac{11}{5} \)[/tex] (After dividing by 9)
- Simplify the ratio of money:
[tex]\( \frac{44}{20} = \frac{11}{5} \)[/tex] (After dividing by 4)
Both ratios simplify to the same, so the statement is true.
(d) 32 m : 64 m = 6 sec : 12 sec
Simplifying each side, we get:
- Simplify the ratio of meters:
[tex]\( \frac{32}{64} = \frac{1}{2} \)[/tex]
- Simplify the ratio of seconds:
[tex]\( \frac{6}{12} = \frac{1}{2} \)[/tex]
Both ratios are equal, meaning the statement is true.
(e) 45 km : 60 km = 12 hours : 15 hours
Let’s simplify this one:
- Simplify the ratio of kilometers:
[tex]\( \frac{45}{60} = \frac{3}{4} \)[/tex]
- Simplify the ratio of hours:
[tex]\( \frac{12}{15} = \frac{4}{5} \)[/tex]
These simplified ratios are not equal, so the statement is false.
So, the results are:
- (a) True
- (b) True
- (c) True
- (d) True
- (e) False
(a) 40 persons : 200 persons = ₹15 : ₹75
To determine if the ratios are equal, we can simplify each ratio:
- Simplify the ratio of persons:
[tex]\( \frac{40}{200} = \frac{1}{5} \)[/tex]
- Simplify the ratio of money:
[tex]\( \frac{15}{75} = \frac{1}{5} \)[/tex]
Since both simplified ratios are equal, the statement is true.
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
Let's simplify each ratio as well:
- Simplify the ratio of litres:
[tex]\( \frac{7.5}{15} = \frac{1}{2} \)[/tex]
- Simplify the ratio of kilograms:
[tex]\( \frac{5}{10} = \frac{1}{2} \)[/tex]
Both simplified ratios are equal, so this statement is true.
(c) 99 kg : 45 kg = ₹44 : ₹20
For this statement, simplify each:
- Simplify the ratio of kilograms:
[tex]\( \frac{99}{45} = \frac{11}{5} \)[/tex] (After dividing by 9)
- Simplify the ratio of money:
[tex]\( \frac{44}{20} = \frac{11}{5} \)[/tex] (After dividing by 4)
Both ratios simplify to the same, so the statement is true.
(d) 32 m : 64 m = 6 sec : 12 sec
Simplifying each side, we get:
- Simplify the ratio of meters:
[tex]\( \frac{32}{64} = \frac{1}{2} \)[/tex]
- Simplify the ratio of seconds:
[tex]\( \frac{6}{12} = \frac{1}{2} \)[/tex]
Both ratios are equal, meaning the statement is true.
(e) 45 km : 60 km = 12 hours : 15 hours
Let’s simplify this one:
- Simplify the ratio of kilometers:
[tex]\( \frac{45}{60} = \frac{3}{4} \)[/tex]
- Simplify the ratio of hours:
[tex]\( \frac{12}{15} = \frac{4}{5} \)[/tex]
These simplified ratios are not equal, so the statement is false.
So, the results are:
- (a) True
- (b) True
- (c) True
- (d) True
- (e) False
