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SCERT Class 7 Maths Chapter 13 Solutions Percents
Class 7 Maths Chapter 13 Percents Questions and Answers Kerala State Syllabus
Percents Class 7 Questions and Answers Kerala Syllabus
Page 183
Question 1.
An electronics manufacturer sells some of their older models at reduced prices, as shown in the table below:
Compute the current price of each.
Answer:
So first we want to find current price of laptop,
For that 1st we want to find how much is 10% of 65000
ie, 65000 × \(\frac{10}{100}\) = 6500
So, current price of laptop = 65000 – 6500
= 58500 rupees
Next, we want to find Current price of mobile phone For that we want to find how much is 20% of 25000
ie, 25000 × \(\frac{20}{100}\) = 5000
Current price of Mobile phone = 25000 – 5000
= 20,000 rupees
Next, we want to find current price of smart watch
So we want to find how much is 30% of 12000 ie, 12000 × \(\frac{30}{100}\) = 3600
Current price of Mobile phone = 12000 – 3600
= 8400
Question 2.
A businessman donates 2% of his monthly profits to charity. In a certain month he got 25000 rupees as profit. How much of this did he donate to charity?
Answer:
Profit he got = 25000 rupees
Amount he donate to charity = 25000 × \(\frac{2}{100}\)
= 500 rupees
So he donate 500 rupees to charity.
Question 3.
i. Persons earning between two and a half lakhs and five lakhs annually, must pay five percent of this as income tax. How much income tax should a person with annual income three and a half lakhs pay?
ii. Persons earning between five and ten lakhs should pay five percent of five lakhs and twenty percent of the excess over five lakhs. How much income tax should a person with annual income seven and a half lakhs pay?
Answer:
i. For that we want to find 5% of 350000
i.e 350000 × \(\frac{5}{100}\) = 17500 100
So a person with annual income three and a half lakhs should pay 17500 rupees as income tax.
ii. So first we want to find 5% of 500000
= 500000 × \(\frac{5}{100}\)
= 25000 rupees
Excess over five lakhs = 150000 -500,000
= 250000 rupees
Tax on excess = 20% of 250000
= \(\frac{20}{100}\) × 250000
= 50000 rupees
Total Tax = Tax on first 5 lakhs + Tax on excess
Total Tax = 25000 + 50000
= 75000 rupees
So, the person with annual income seven and half lakhs should pay 75000 rupees as income tax.
Page 184
Question 1.
Of the 50 teachers in a school, 80% are women. How many female teachers are there in the school?
Answer:
Number of female teachers in the school = 50 × \(\frac{80}{100}\)
= 40
Question 2.
1450 persons voted in an election contested by two persons. The winner got 52% of the votes
i. How many votes did he get?
ii. By how many votes did he win?
Answer:
i. Votes for the winner = 52% of 1450
= 1450 × \(\frac{52}{100}\)
ii. Votes for the loser =1450 – 754 = 696
Margin of victory = Votes for the winner – Votes for the loser
= 754 – 696
= 58
Question 3.
1200 kids took an exam and 65% of them got A grade. How many are they?
Answer:
Number of kids with A grade = 65% of 1200
= \(\frac{65}{100}\) × 1200 = 780
Question 4.
There are 32 coconut palms in a compound. This is 50% of the total number of trees in the compound. What is the total number of trees?
Answer:
50% = \(\frac{50}{100}=\frac{1}{2}\) of total trees are coconut palms
So the total no. of trees in the compound is \(\frac{2}{1}\) times the number of coconut palm in the compound.
So, the total number of trees in the compound is \(\frac{2}{1}\) × 32
= 2 × 32
= 64
Question 5.
A person spends 8400 rupees a month for food. It is 25% of his monthly earnings. What is his monthly earnings?
Answer:
25% = \(\frac{25}{100}=\frac{1}{4}\) of the total monthly earning spent for food,
So the total monthly earning is \(\frac{4}{1}\) times the money spent for food.
So, monthly earning = \(\frac{4}{1}\) × 8400
= 4 × 8400
= 33600 rupees
Page 187
Question 1.
A bicycle originally priced at 4000 rupees is now sold for 15% less. What is the current price?
Answer:
Sold for 15% less means 85%
ie, \(\frac{1}{2}\) of the original
So, the current price = \(\frac{17}{20}\) × old price
= \(\frac{17}{20}\) × 4000
= 3400 rupees
Question 2.
The monthly salary of a person was 30000 rupees last year. This year, he got an 8% raise. What is his monthly salary now?
Answer:
He got an 8% raise means 100 + 8 = 108 %
ie , \(\frac{108}{100}\) times the original
So, current salary = \(\frac{108}{100}\) × 30000
= 32400 rupees
Question 3.
If the height and width of a rectangle are reduced by 10% each, by what percent would the area be reduced?
Answer:
Let the original height and width of a rectangle be h and w respectively
So original area = h × w
Height and width of a rectangle are reduced by 10% each
Reduced by 10% each means 90 % = \(\frac{1}{2}\)
Thus new height = \(\frac{9}{10}\) × original height = \(\frac{9}{10}\) × h
New width = \(\frac{9}{10}\) × original width = \(\frac{9}{10}\) = w
Therefore, New Area = New height × New width
= (\(\frac{9}{10}\) × h) × (\(\frac{9}{10}\) × w)
= \(\frac{81}{100}\) × h × w
= \(\frac{81}{100}\) × Orginal area
So, the area is reduced by 19%.
Question 4.
If the height and width of a rectangle are increased by 10% each, by what percent would the area be increased?
Answer:
Let the original height and width of a rectangle be h and w respectively
Original Area = h × w
The new height and width are increased by 10% each
10% increase means \(\frac{110}{100}=\frac{11}{10}\)
New height = \(\frac{11}{10}\) × original height = \(\frac{11}{10}\) × h
New width = \(\frac{11}{10}\) × original width = \(\frac{11}{10}\) × w
New Area = (\(\frac{11}{10}\) × original height × (\(\frac{11}{10}\) × original width
= (\(\frac{11}{10}\) × h) × (\(\frac{11}{10}\) × w)
= \(\frac{121}{100}\) × h × w
= \(\frac{121}{100}\) × Orginal area
So, the area is increased by 21%.
Page 188
Question 1.
Can you write as fractions, the parts given as percents below?
Answer:
Now let’s see how we can convert a part expressed as a percent into a fraction,
For example, the fractional form of the part given as 33 – % can be computed like this:
\(\frac{1}{100}\) × 33\(\frac{1}{3}\)
= \(\frac{1}{100} \times \frac{100}{3}\)
= \(\frac{1}{3}\)
Thus 33\(\frac{1}{3}\) % of a number is \(\frac{1}{3}\) of that number.
Page 190
Question 1.
In a school there are 750 students and 450 of them are girls. What is the percent of girl students?
Answer:
Percentage of girls =\(\frac{450}{750}\) × 100
Percentage of girls = \(\frac{9}{15}\) × 100 = 60%
Question 2.
A person who earns 30000-rupees a month spends 8000 rupees on food. What percent of the earnings is this?
Answer:
Percentage spent on food = \(\frac{8000}{30000}\) × 100
Here, the amount spent on food is 8000 rupees, and the total earnings are 30000 rupees.
Percentage = (\(\frac{8000}{30000}\)) × 100
(\(\frac{8}{30}\)) × 100
= 26\(\frac{2}{3}\) %
Question 3.
If a bicycle bought for 4500 rupees had to be sold for 4000 rupees, what is the loss percent?
Answer:
Loss = 4500 – 4000 = 500 rupees
Loss percent = (\(\frac{500}{4500}\)) × 100
= \(\frac{5}{45}\) × 100
= 11\(\frac{1}{9}\)%
Question 4.
1600 persons voted in an election and the winner got 900 votes. What percent of the total votes is this?
Answer:
Votes for Winner = 900
Total Votes = 1600
Percentage = \(\frac{900}{1600}\) × 100
= \(\frac{9}{16}\) × 100
= 56\(\frac{1}{4}\)%
= 56.25 %
Question 5.
Ajayan’s salary is 25 % more than sajayan’s salary. By what percent of Ajayan’s salary is Sajayan’s salary less?
Answer:
Let’s Sajayan’s salary be 100 units.
Since Ajayan’s salary is 25% more
Then Ajanyan’s salary = 100 + 25 = 125 units
Percentage of decrease in salary = \(\frac{125-100}{125}\) × 100
= \(\frac{25}{125}\) × 100 = 20%
So Sajayan’s salary is 20% less than Ajayan’s salary
Intext Questions And Answers
Question 1.
During Vaccation time, there is 30% reduction in the price of books. What is the reduction for 2350 rupees worth of books?
Answer:
For any price, the reduction is 30 times the number of 100’s in it.
That is, 30 times \(\frac{1}{100}\) of the price, which means \(\frac{30}{100}\) of the price.
\(\frac{1}{2}\)
Thus reduction is \(\frac{3}{10}\) of the price.
\(\frac{3}{10}\) of 2350 is
\(\frac{3}{10}\) × 2350 = \(\frac{3 \times 2350}{10}=\frac{3 \times 235 \times 10}{10}\)
= 235 × 3
= 705
The reduction for 2350 rupees is 705 rupees
Question 2.
In a co-operative bank, fixed deposits for a year are given 6% interest. If 5500 rupees are deposited, how much would be got after one year?
Answer:
Here 6 is \(\frac{6}{100}\) of 100
Therefore interest = \(\frac{6}{100}\) of 5500
\(\frac{6}{100}\) × 5500
= \(\frac{6 \times 55 \times 100}{100}\)
= 330
Another way is decimal computation,
ie, \(\frac{6}{100}\) = 0.06
So, 0.06 × 5500 = 330
So if 5500 rupees are deposited, then amount got after one year, including interest is,
5500 + 330 = 5830 rupees
Question 3.
In the tables below, the fractional forms of some commonly used percent are given . Can you fill in the second table?
Answer:
Question 4.
A scooter manufacturer has decided to increase the price by 5% from next month. For a scooter now selling for 120000 rupees, what would be the price next month?
Answer:
The increase is \(\frac{5}{100}\) of the current price
of a number added to it, makes it \(\frac{105}{100}\) times the original
So the new price is ^ times the current price ‘
\(\frac{105}{100}\) times 120000 is 100
\(\frac{105}{100}\) × 120000 = 105 × 1200 = 105 × 12 × 100 = 126000
Thus the price in the next month would be 126000 rupees.
Now let’s see another problem,
Question 5.
The width of a rectangle is increased by 10% and the height decreased by 10%, to make a new rectangle. What is the change in area?
Answer:
Increasing by 10% means becoming 110%
110% = \(\frac{110}{100}=\frac{11}{10}\) of the original
New width = \(\frac{11}{10}\) × Old width 10
Decreasing by 10% means becoming 90%
90% = \(\frac{90}{100}=\frac{9}{10}\) of the original 100 10 6
New height = \(\frac{9}{10}\) × Old height
New area = New width × New height
= (\(\frac{11}{10}\) × Old width) × (\(\frac{9}{10}\) × Old height)
= \(\frac{11}{10} \times \frac{9}{10}\) × (Old width × Old height)
= \(\frac{99}{100}\) × Old area
= 99% of the old area
So the area is reduced by 1%
Question 6.
To convert a part expressed as a percent to the fractional form, \(\frac{1}{100}\) of that number is to be computed.
Now let’s see how we can convert fraction into percent
So, let’s check how do we write ^ of a number as a percent of that number?
Answer:
\(\frac{1}{3}\) (of a number) is \(\frac{1}{100}\) of the percent (of that number)
So, the percent is 100 times \(\frac{1}{3}\)
That is
100 × \(\frac{1}{3}=\frac{100}{3}\) = 33\(\frac{1}{3}\)
Thus \(\frac{1}{3}\) of a number is 33 \(\frac{1}{3}\) % of that number.
Question 7.
If a furniture set bought for 50000 rupees is sold for 50550 rupees, what is the profit percent?
Answer:
The actual profit = 50550 – 50000 = 550 rupees
That is \(\frac{550}{50000}\) × 100 = \(\frac{55}{50}\) = 1\(\frac{1}{10}\)
So profit is 1\(\frac{1}{10}\) %
Another way to write it is like this \(\frac{55}{50}\) = 1.1
So that profit is 1.1%
In general,
To convert a part expressed as a fraction to a percent, 100 times the fraction must be computed
Class 7 Maths Chapter 13 Kerala Syllabus Percents Questions and Answers
Question 1.
A shopkeeper deposit 12% of his monthly profits to orphanage. In a certain month he got 60000 rupees as profit. How much of this did he donate to orphanage?
Answer:
His profit = 60000
12% of his profit = 60000 × \(\frac{12}{100}\)
= 7200
So he donate 7200 rupees to orphanage.
Question 2.
A person spends 5000 rupees a month for food. It is 20% of his monthly earnings. What is his monthly earnings?
Answer:
20% = \(\frac{1}{2}\) of the monthly earning spend for food.
So the total monthly is \(\frac{5}{1}\) times the money spent for food
So, monthly earning = \(\frac{5}{1}\) × 5000 = 2500 rupees
Question 3.
A shirt originally priced at 800 rupees is now sold for 20% less. What is the current price?
Answer:
Selling for 20% less means the new price is 80% of the original price.
ie \(\frac{80}{100}=\frac{4}{5}\)
Current Price = \(\frac{4}{5}\) × 800 .
= \(=\frac{4 \times 800}{5}\)
= \(\frac{3200}{5}\)
= 640 rupees
Question 4.
A person who earns 45,000 rupees a month spends 10,500 rupees on rent. What percent of their earnings does this spending represent?
Answer:
Percentage = \(\left(\frac{10,500}{45,000}\right)\) × 100
\(\frac{10,500}{45,000}=\frac{105}{450}=\frac{7}{30}\)
Percentage = (\(\left(\frac{7}{30}\right)\)) × 100
= 23\(\frac{1}{3}\)% = 23.33%
Class 7 Maths Chapter 13 Notes Kerala Syllabus Percents
Welcome to the exciting world of percents! In this chapter, we will explore one of the most useful concepts in mathematics that helps us understand proportions and comparisons in everyday life. Percents are a way of expressing a number as a fraction of 100. The term “percent” itself means “per hundred.” You encounter percents in various real-life situations, such as calculating discounts during shopping, understanding statistics in sports, and analyzing data in reports.
In this chapter, you will learn how to:
- Convert fractions and decimals into percents.
- Calculate percentages of a given number.
- Determine how to find percentage increase or decrease.
- Solve real-life problems using percent calculations.
By the end of this chapter, you’ll have a solid grasp of percents, enabling you to tackle a variety of mathematical challenges and apply this knowledge in real-world situations.
Percents And Fractions
In the previous classes we discuss about percents and some of its uses. Here we are going to discuss more about this topic Percents. Percents are a way to express a number as a part of 100. The term “percent” literally means “per hundred. “We can represent percents as fractions.
Now let’s look another instant where percents are used:
If we deposit money in banks and withdraw it after a specified time, we get some extra amount called the interest. The extra amount when loans are repaid is also interest.
Some Other Percents
We use percents in many situation, not only in money matters. Here are some examples of how percents are used in our daily lives.
- Finance: Interest rates, loan terms, and investment returns often use percentages. For instance, a savings account might offer 2% interest.
- Shopping: Discounts are typically presented in percentages, like a 30% off sale on clothing.
- Statistics: In surveys or studies, results are often summarized as percentages, such as 65% approval ratings.
- Nutrition: Food labels often display percentages of daily values based on a standard diet.
For example,
In a class of 80 students 60% passed an exam.
We know that 60% = \(\frac{60}{100}\)
= \(\frac{6}{10}\)
= \(\frac{3}{5}\)
So the actual number of students who passed the exam = 80 × \(\frac{3}{5}\)
= 48
Therefore 48 students passed the exam.
Less And More
Here we are going to discuss less and more concept through some examples, This example illustrates how a simple percentage increase or decrease can significantly affect the final cost.
Fractions And Percents
Percent means hundredths multiplied by a specific number.
For example 99% of a number means \(\frac{99}{100}\) of that number, and that is 99 times \(\frac{1}{100}\) of that number.
Understanding fractions and percents is crucial for everyday math.
Employees in public sector undertakings are given an extra amount, in addition to salary, every year. It is called bonus. Usually it is 8 \(\frac{1}{3}\) %. What fraction of the annual salary is this?
Answer:
8 \(\frac{1}{3}\) times \(\frac{1}{100}\).
That is, 8\(\frac{1}{3}\) x \(\frac{1}{100}\) = \(\frac{25}{3}\) x \(\frac{1}{100}\)
= \(\frac{1}{2}\)
= \(\frac{1}{12}\)
So 8 \(\frac{1}{3}\) % of a number is \(\frac{1}{12}\) of that number.
- To convert a part expressed as a percent to the fractional form, ^ of that number is to be computed.
- To convert a part expressed as a fraction to a percent, 100 times the fraction must be computed.