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Sagot :
Let's address each problem step-by-step.
### 1. Finding the Ratios
#### (a) Speed of a cycle 15 km per hour to the speed of a scooter 30 km per hour
To find the ratio of the cycle's speed to the scooter's speed:
[tex]\[ \text{Ratio} = \frac{\text{Speed of cycle}}{\text{Speed of scooter}} = \frac{15}{30} \][/tex]
The ratio simplifies to:
[tex]\[ \text{Ratio} = 0.5 \][/tex]
#### (b) 5 meters to 10 kilometers
Since 1 kilometer equals 1000 meters, we first convert 10 km to meters:
[tex]\[ 10 \, \text{km} = 10 \times 1000\, \text{m} = 10000 \, \text{m} \][/tex]
Then we find the ratio:
[tex]\[ \text{Ratio} = \frac{5 \, \text{m}}{10000 \, \text{m}} = \frac{5}{10000} \][/tex]
The ratio simplifies to:
[tex]\[ \text{Ratio} = 0.0005 \][/tex]
#### (c) 50 paise to ₹5
Since 1 rupee equals 100 paise, we first convert ₹5 to paise:
[tex]\[ 5 \, \text{₹} = 5 \times 100 \, \text{paise} = 500 \, \text{paise} \][/tex]
Then we find the ratio:
[tex]\[ \text{Ratio} = \frac{50 \, \text{paise}}{500 \, \text{paise}} = \frac{50}{500} \][/tex]
The ratio simplifies to:
[tex]\[ \text{Ratio} = 0.1 \][/tex]
### 2. Converting Ratios to Percentages
#### (a) [tex]$3: 4$[/tex]
To convert the ratio [tex]\( \frac{3}{4} \)[/tex] to a percentage:
[tex]\[ \text{Percentage} = \left( \frac{3}{4} \right) \times 100 = 75.0 \% \][/tex]
#### (b) [tex]$2: 3$[/tex]
To convert the ratio [tex]\( \frac{2}{3} \)[/tex] to a percentage:
[tex]\[ \text{Percentage} = \left( \frac{2}{3} \right) \times 100 = 66.67 \% \][/tex]
### 3. Students Interested in Mathematics
#### 72% of 25 students are interested in mathematics. How many are not interested in mathematics?
First, find 72% of 25:
[tex]\[ \text{Interested students} = 0.72 \times 25 = 18 \][/tex]
The number of students not interested in mathematics:
[tex]\[ \text{Not interested} = 25 - 18 = 7 \][/tex]
So, 7 students are not interested in mathematics.
### 4. Football Team's Total Matches Played
#### A football team won 10 matches out of the total number of matches they played. If their win percentage was 40%, then how many matches did they play in all?
Let's denote the total number of matches played by [tex]\( x \)[/tex]. Given the win percentage is 40%, we have:
[tex]\[ 0.4x = 10 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{10}{0.4} = 25 \][/tex]
So, the team played a total of 25 matches.
### 5. Chameli's Initial Amount of Money
#### Chameli had ₹600 left after spending 75% of her money. How much did she have initially?
Let the initial amount be [tex]\( x \)[/tex]. After spending 75%, she has 25% of her money left:
[tex]\[ 0.25x = 600 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{600}{0.25} = 2400 \][/tex]
So, Chameli initially had ₹2400.
This completes the detailed, step-by-step solutions for the given problems.
### 1. Finding the Ratios
#### (a) Speed of a cycle 15 km per hour to the speed of a scooter 30 km per hour
To find the ratio of the cycle's speed to the scooter's speed:
[tex]\[ \text{Ratio} = \frac{\text{Speed of cycle}}{\text{Speed of scooter}} = \frac{15}{30} \][/tex]
The ratio simplifies to:
[tex]\[ \text{Ratio} = 0.5 \][/tex]
#### (b) 5 meters to 10 kilometers
Since 1 kilometer equals 1000 meters, we first convert 10 km to meters:
[tex]\[ 10 \, \text{km} = 10 \times 1000\, \text{m} = 10000 \, \text{m} \][/tex]
Then we find the ratio:
[tex]\[ \text{Ratio} = \frac{5 \, \text{m}}{10000 \, \text{m}} = \frac{5}{10000} \][/tex]
The ratio simplifies to:
[tex]\[ \text{Ratio} = 0.0005 \][/tex]
#### (c) 50 paise to ₹5
Since 1 rupee equals 100 paise, we first convert ₹5 to paise:
[tex]\[ 5 \, \text{₹} = 5 \times 100 \, \text{paise} = 500 \, \text{paise} \][/tex]
Then we find the ratio:
[tex]\[ \text{Ratio} = \frac{50 \, \text{paise}}{500 \, \text{paise}} = \frac{50}{500} \][/tex]
The ratio simplifies to:
[tex]\[ \text{Ratio} = 0.1 \][/tex]
### 2. Converting Ratios to Percentages
#### (a) [tex]$3: 4$[/tex]
To convert the ratio [tex]\( \frac{3}{4} \)[/tex] to a percentage:
[tex]\[ \text{Percentage} = \left( \frac{3}{4} \right) \times 100 = 75.0 \% \][/tex]
#### (b) [tex]$2: 3$[/tex]
To convert the ratio [tex]\( \frac{2}{3} \)[/tex] to a percentage:
[tex]\[ \text{Percentage} = \left( \frac{2}{3} \right) \times 100 = 66.67 \% \][/tex]
### 3. Students Interested in Mathematics
#### 72% of 25 students are interested in mathematics. How many are not interested in mathematics?
First, find 72% of 25:
[tex]\[ \text{Interested students} = 0.72 \times 25 = 18 \][/tex]
The number of students not interested in mathematics:
[tex]\[ \text{Not interested} = 25 - 18 = 7 \][/tex]
So, 7 students are not interested in mathematics.
### 4. Football Team's Total Matches Played
#### A football team won 10 matches out of the total number of matches they played. If their win percentage was 40%, then how many matches did they play in all?
Let's denote the total number of matches played by [tex]\( x \)[/tex]. Given the win percentage is 40%, we have:
[tex]\[ 0.4x = 10 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{10}{0.4} = 25 \][/tex]
So, the team played a total of 25 matches.
### 5. Chameli's Initial Amount of Money
#### Chameli had ₹600 left after spending 75% of her money. How much did she have initially?
Let the initial amount be [tex]\( x \)[/tex]. After spending 75%, she has 25% of her money left:
[tex]\[ 0.25x = 600 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{600}{0.25} = 2400 \][/tex]
So, Chameli initially had ₹2400.
This completes the detailed, step-by-step solutions for the given problems.
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