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In our daily life, there are many occasions when we compare two quantities. What is the name of this comparison?
In our daily life, there are many occasions when we compare two quantities. What is the name of this comparison?
Ratio
If Heena is two times taller than Amir, what is the ratio of their heights?
If Heena is two times taller than Amir, what is the ratio of their heights?
2:1
What is the ratio of 3 km to 300 m?
What is the ratio of 3 km to 300 m?
10:1
What is the ratio of wins to losses for the cricket team in the last year?
What is the ratio of wins to losses for the cricket team in the last year?
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What is the ratio of wins to losses for the cricket team in the current year?
What is the ratio of wins to losses for the cricket team in the current year?
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The ratio 1:2 is equivalent to the ratio 2:3.
The ratio 1:2 is equivalent to the ratio 2:3.
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In the making of national flags, the ratio of length to breadth is mostly around ______ or ______.
In the making of national flags, the ratio of length to breadth is mostly around ______ or ______.
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The ratio 4.5:3.0 is equivalent to the ratio 3:2.
The ratio 4.5:3.0 is equivalent to the ratio 3:2.
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A map has a scale of 2 cm = 1000 km. What is the actual distance between two places if the distance on the map is 2.5 cm?
A map has a scale of 2 cm = 1000 km. What is the actual distance between two places if the distance on the map is 2.5 cm?
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If 6 bowls cost ₹90, what is the cost of 10 bowls?
If 6 bowls cost ₹90, what is the cost of 10 bowls?
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If a car can travel 150 km with 25 litres of petrol, how far can it travel with 30 litres of petrol?
If a car can travel 150 km with 25 litres of petrol, how far can it travel with 30 litres of petrol?
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An ant can carry 50 times its weight. If a person can do the same, how much would a person weighing 50 kg be able to carry?
An ant can carry 50 times its weight. If a person can do the same, how much would a person weighing 50 kg be able to carry?
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What is the ratio of 5 to 50 paise?
What is the ratio of 5 to 50 paise?
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What is the ratio of 15 kg to 210 g?
What is the ratio of 15 kg to 210 g?
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What is the ratio of 9 m to 27 cm?
What is the ratio of 9 m to 27 cm?
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What is the ratio of 30 days to 36 hours?
What is the ratio of 30 days to 36 hours?
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In a computer lab, there are 3 computers for every 6 students. How many computers are needed for 24 students?
In a computer lab, there are 3 computers for every 6 students. How many computers are needed for 24 students?
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The population of Rajasthan is 570 lakhs and the population of UP is 1660 lakhs. What is the population density of Rajasthan (people per square kilometer)?
The population of Rajasthan is 570 lakhs and the population of UP is 1660 lakhs. What is the population density of Rajasthan (people per square kilometer)?
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The population of Rajasthan is 570 lakhs and the population of UP is 1660 lakhs. What is the population density of UP (people per square kilometer)?
The population of Rajasthan is 570 lakhs and the population of UP is 1660 lakhs. What is the population density of UP (people per square kilometer)?
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Which state (Rajasthan or Uttar Pradesh) is less populated?
Which state (Rajasthan or Uttar Pradesh) is less populated?
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What does the symbol '%' represent?
What does the symbol '%' represent?
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What is the fractional equivalent of 1%?
What is the fractional equivalent of 1%?
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What is the decimal equivalent of 1%?
What is the decimal equivalent of 1%?
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In Rina's table, what percentage of tiles are red?
In Rina's table, what percentage of tiles are red?
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What is the percentage of the total number of children whose height is 128 cm?
What is the percentage of the total number of children whose height is 128 cm?
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In Mala's collection of bangles, what is the percentage of gold bangles?
In Mala's collection of bangles, what is the percentage of gold bangles?
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What is 3/5 expressed as a percentage?
What is 3/5 expressed as a percentage?
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A class has 25 children, and 15 are girls. What is the percentage of girls in the class?
A class has 25 children, and 15 are girls. What is the percentage of girls in the class?
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If 12 out of 32 students are absent, what percentage of students are absent?
If 12 out of 32 students are absent, what percentage of students are absent?
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Out of 25 radios, 16 are out of order. What percentage of radios are out of order?
Out of 25 radios, 16 are out of order. What percentage of radios are out of order?
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If a shop has 500 items and 5 are defective, what percentage of items are defective?
If a shop has 500 items and 5 are defective, what percentage of items are defective?
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If there are 120 voters and 90 of them voted yes, what percentage of voters voted yes?
If there are 120 voters and 90 of them voted yes, what percentage of voters voted yes?
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If 65% of students in a class have a bicycle, what percentage of students do not have a bicycle?
If 65% of students in a class have a bicycle, what percentage of students do not have a bicycle?
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If 50% of a basket of fruit consists of apples and 30% are oranges, what percentage of the fruit are mangoes?
If 50% of a basket of fruit consists of apples and 30% are oranges, what percentage of the fruit are mangoes?
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If a shopkeeper bought a chair for ₹375 and sold it for ₹400, what is the gain percentage?
If a shopkeeper bought a chair for ₹375 and sold it for ₹400, what is the gain percentage?
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An item was sold for ₹250 with a profit of 5%. What was the cost price of the item?
An item was sold for ₹250 with a profit of 5%. What was the cost price of the item?
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If an article is sold for ₹540 at a loss of 5%, what was the cost price of the item?
If an article is sold for ₹540 at a loss of 5%, what was the cost price of the item?
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If Anita takes a loan of ₹5,000 at 15% per year, how much interest does she have to pay at the end of one year?
If Anita takes a loan of ₹5,000 at 15% per year, how much interest does she have to pay at the end of one year?
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If ₹10,000 is invested at a 5% interest rate per annum, how much interest will be earned at the end of one year?
If ₹10,000 is invested at a 5% interest rate per annum, how much interest will be earned at the end of one year?
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If ₹3,500 is invested at 7% per annum, how much interest will be earned at the end of two years?
If ₹3,500 is invested at 7% per annum, how much interest will be earned at the end of two years?
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If ₹6,050 is borrowed at a 6.5% annual interest rate, how much interest will be paid at the end of three years?
If ₹6,050 is borrowed at a 6.5% annual interest rate, how much interest will be paid at the end of three years?
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If ₹7,000 is borrowed at a 3.5% annual interest rate, how much interest will be paid at the end of two years?
If ₹7,000 is borrowed at a 3.5% annual interest rate, how much interest will be paid at the end of two years?
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If Manohar pays an interest of ₹750 for 2 years on a sum of ₹4,500, what is the rate of interest?
If Manohar pays an interest of ₹750 for 2 years on a sum of ₹4,500, what is the rate of interest?
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You have ₹2,400 in your account and the interest rate is 5%. After how many years will you earn ₹240 as interest?
You have ₹2,400 in your account and the interest rate is 5%. After how many years will you earn ₹240 as interest?
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Study Notes
Comparing Quantities
- Comparing quantities is common in daily life.
- Comparing heights: Heena is two times taller than Amir, or Amir's height is half of Heena's height.
- Comparing marbles: Rita has 12 marbles and Amit has 8 marbles; Rita has 1.5 times the marbles Amit has.
- Comparing speeds: A cheetah's speed is 6 times the speed of a man, or a man's speed is one-sixth of the cheetah's speed.
- Comparing quantities can be expressed as how many times one quantity is of the other. This can also be inverted as what part one quantity is of the other.
Equivalent Ratios
- Ratios with the same value can represent different situations, as long as the units are the same.
- Ratios have no units.
- Example: find the ratio of 3 km to 300 m. The ratio would be 10:1.
Percentages
- Percentage means 'per hundred'.
- Percentages are numerators of fractions with a denominator of 100.
- 1% = 1/100 = 0.01.
- Percentages are used for comparing results
Converting Decimals to Percentages
- Multiply the decimal value by 100.
- Example: 0.75 = 75%
Converting Fractions to Percentages
- Multiply the fraction by 100%. This does not change the value of the fraction.
- Example: 3/5 = 0.6 X 100% = 60%.
Percentages of an Amount
- Find the number by multiplying the fraction by the total amount.
- Example: 25% of 40 children = 0.25 × 40 = 10 children
Increase or Decrease as Percentage
- Calculate the increase or decrease.
- Divide the difference by the original amount.
- Multiply by 100 to get the percentage.
- Example: If a sweater's price dropped from ₹200 to ₹150, the decrease is ₹50. (200-150) / 200 = 0.25 X 100 = 25% decrease.
Cost Price, Selling Price, Profit and Loss
- Cost Price (CP): The price at which an item is bought.
- Selling Price (SP): The price at which an item is sold.
- Profit = SP – CP
- Loss = CP – SP
- Profit/Loss Percentage is calculated on the Cost Price.
Simple Interest
- Simple interest is calculated on the principal amount for a specified period.
- Formula: Simple Interest = (P × R × T) / 100 P = Principal amount R = Rate of Interest T= Time(in years)
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Description
This quiz covers essential concepts in mathematics related to comparing quantities, equivalent ratios, and percentages. You will learn how to express relationships between different quantities and understand how to convert decimals to percentages. Test your knowledge on how these concepts apply to everyday situations.
