RD Sharma Class 7 Maths Solutions Chapter 11 - Percentage

RD Sharma Class 7 Chapter 11  Percentage is provided here. This exercise has included verbally based questions based on the topic of a percentage to solve real-life problems. It also covers concepts with an increase or decrease in percentage. In this exercise, students will understand the meaning of per cent and the concept of percentage. This chapter mainly deals with the conversion of a percentage into a fraction and vice versa.

Following Are Some of the Important Concepts That Are Being Discussed in This Chapter.

• Meaning of percent

• Percent as a fraction

• Percent as a ratio

• Conversion of percent into a fraction

• Conversion of a fraction into percentage

• Conversion of a ratio into percentage and vice versa

• Conversion of a percentage into a decimal and vice versa

• Finding the percentage of a given number

• Some word problems on percentage

Meaning of percent

Percentage is an approximate value indicating the hundredth parts of any quantity. It means a number or a ratio represented in the form of fractions of 100. It is followed by the percentage sign ‘%’. Percentage can be expressed using abbreviations such as ‘pct’ or ‘pc’. In other words, the percentage is described as how much one quantity comprises another quantity and it is represented in terms of 100.

The percentage is a dimensionless quantity. If we say 80% of a number, then it means 80 per cent of the whole. It can even be expressed in decimal and fraction forms too. One real-life scenario where percentages are used is in our schools to assess our performance through our marks. For example-Manika scored 98% of marks in her exam. So, this percentage is calculated in terms of total marks obtained by Manika in all the subjects to the total maximum marks and then the result will be multiplied by 100. 

Percent as a fraction

We can express percentages in terms of fractions too. For example, if we represent 8% in the form of a fraction, it will be 8 parts of 100 or \[\frac{8}{100}\]. 

Percent as a ratio

Percentages like fractions can be expressed in terms of ratios too. It’s very easy to do so. We first write the percentage in the form of x:y. Where x is the given percentage and y is 100.

Conversion of percent into a fraction

In order to convert percent into a fraction, we need to put the values in the given formula.

Percent to fraction formula:

\[ Fraction =\frac{(Given Percentage)}{100}\]

Let’s understand this better with the help of an illustration:

Represent 25% in terms of a fraction.

Here, 20% can be represented as \[\frac{25}{100}\] which is then simplified to get the desired fraction.

\[\frac{25}{100}=\frac{1}{4}\]

Thus the fraction comes out to be \[\frac{1}{4}\].

Conversion of a fraction into a percentage

We can convert a fraction into a percentage too. In order to convert percent into a fraction, we need to put the values in the given formula.

\[Percentage = Fraction\times  100=(\frac{1}{4})\times  100=25\]%

Thus the answer is 25%.

Conversion of a percent to ratio and vice versa

Per cent can easily be converted into a ratio and vice versa by the following steps.

Percent to ratio formula:

Ratio= Given percentage: 100

Let’s understand this better with the help of an illustration. 

Convert 25 per cent to a ratio. 

To do so, we put 25 in the place of x and 100 in the place of y in the x:y format. 

25:100

On simplifying, we get-

1:4

In order to convert the ratio to percent, we first need to convert the ratio to a fraction and follow the steps of conversion of a fraction to a percentage.

Ratio to percent formula:

Ratio = x:y

\[Fraction =\frac{x}{y}\]

\[Percent = \frac{x}{y}\times100\]

Let’s understand this better with the help of an illustration.

Convert 1:4 to a percentage.

Here, we convert 1:4 to a fraction, \[\frac{1}{4}\]

Then we multiply 100 to the fraction.

\[(\frac{1}{4})\times\] 100=25%

Conversion of a percentage into a decimal and vice versa

We can convert a percentage into a decimal and vice versa by following the given steps. Let us see how to convert percent to decimal.

Percent to decimal formula:

Decimal=\[\frac{Percent}{100}\]

Let us understand this better with the help of an illustration.

Convert 17% to decimal.

In order to do this we simply divide 17 by 100

\[\Rightarrow\left ( \frac{17}{100} \right )\] = 0.17

Hence, it has been converted to decimal form.

Decimal to percent formula:

Percent = Decimal \[\times\] 100

Let us understand this better with the help of an illustration.

Convert 0.17 to percentage.

Here, we simply have to multiply 100 to the given number.

0.17\[ \times\] 100= 17%

Thus, it comes out to be 17 per cent.

Finding the percentage of a given number

Finding the percentage of a number is very easy. We just have to divide the given number by the total and multiply 100 to it. 

Percentage formula:

\[Percentage=\left ( \frac{Given Number}{Total } \right )\times 100\]

This can be illustrated further with the help of an example.

Suppose we have to find 20% of 21. 

The percentage will be,

Percentage = \[\frac{20}{21}\times100\]

95.238%

Some word problems on percentage

Q.After subtracting a commission of 5%, a moped costs Rs 15200. What is its gross value?

Solution:

Let us suppose that the gross value of the moped is Rs x.

Commission on the moped = 5%

x-5% of x=x-\[\left ( \frac{5x}{100} \right )\]=\[\frac{(100x-5x)}{100}\]=\[\frac{95x}{100}\]

Now, price of the moped after reducing the commission = Rs 15200

Then \[\frac{95x}{100}\]=15200

So, x= Rs \[\frac{(15200\times 100)}{95}\] = Rs (160 \[\times \] 100= Rs 16000

Therefore, the gross value of the moped is Rs 16000.

Q.Michael had a science exam and got 30 correct and 10 incorrect answers. What is the percentage of correct answers?

Solution:

Total number of answers = 30+10= 40

Percentage of correct answers = \[ \frac{30}{40}\times 100\]

=\[\frac{3000}{40}\]

= 75

Therefore, he got 75% of correct answers.

Exercises in RD Sharma Solutions For Class 7 Maths Chapter 11

• Exercise 11.1

• Exercise 11.2

• Exercise 11.3

• Exercise 11.4

• Exercise 11.5

• Exercise 11.6

Conclusion

For students who wish to score high marks in Maths, RD Sharma Solutions is the best study material. The subject matter experts at Vedantu have prepared the  RD Sharma solutions to help the students who are finding difficulties in solving them. Students can easily access answers to the problems present in RD Sharma Class 7 Chapter 11  by downloading the PDF. It contains all solutions in a detailed manner and also expects questions to be asked in the exam. After solving these problems students will get more confident about the exam.