Answer

Verified

436.5k+ views

Hint: Start solving by finding the relation between the first number and the second number. Then find the percentage using the percentage formula or obtain the ratio of second number to the first number and multiply by 100.

Let us first assign the numbers to variables.

Let the first number be denoted by variable \[a\] and the second number be denoted by variable \[b\] .

It is given that the sum of these two numbers is \[\dfrac{{23}}{{20}}\] of the first number.

Let us write the equation as follows:

\[a + b = \dfrac{{23}}{{20}}a{\text{ }}..........(1)\]

Now let us simplify this further to obtain the relationship between the two numbers, \[a\] and \[b\] .

In equation (1), taking \[a\]in the left-hand side of the equation to the right-hand side, we get

\[b = \dfrac{{23}}{{20}}a - a\]

Taking \[a\] as a common term and solving, we get:

\[b = \left( {\dfrac{{23}}{{20}} - 1} \right)a\]

\[b = \left( {\dfrac{{23 - 20}}{{20}}} \right)a\]

\[b = \dfrac{3}{{20}}a{\text{ }}..........{\text{(2)}}\]

Hence, we obtained a relation between \[a\] and \[b\] .

To determine what percentage of the first number is the second number, we need to divide the second number by the first number and multiply the result by 100. This comes from the basic percentage formula as follows:

\[{\text{Percentage}} = \dfrac{{{\text{Required Value}}}}{{{\text{Total Value}}}} \times 100{\text{ \% }}\]

Here, the required value is the second number \[b\] and the total value is the first number \[a\] .

The required formula is as follows:

\[{\text{Percentage}} = \dfrac{b}{a} \times 100{\text{ \% }}...........{\text{(3)}}\]

Substituting equation (2) in equation (3), we get:

\[{\text{Percentage}} = \dfrac{{\dfrac{3}{{20}}a}}{a} \times 100{\text{ \% }}\]

Cancelling \[a\] in the numerator and denominator, we get:

\[{\text{Percentage}} = \dfrac{3}{{20}} \times 100{\text{ }}\% \]

Simplifying further we obtain:

\[{\text{Percentage}} = \dfrac{{300}}{{20}}{\text{ \% }}\]

\[{\text{Percentage}} = 15{\text{ \% }}\]

Hence, the correct answer is option (c).

Note: A common mistake committed is writing the equation as \[a + b = \dfrac{{23}}{{20}}b\] with \[b\] being the second number, which is wrong. You can also proceed by finding the ratio \[\dfrac{b}{a}\] directly from the equation \[b = \dfrac{3}{{20}}a{\text{ }}\] and multiplying the result by 100 to get the final answer.

Let us first assign the numbers to variables.

Let the first number be denoted by variable \[a\] and the second number be denoted by variable \[b\] .

It is given that the sum of these two numbers is \[\dfrac{{23}}{{20}}\] of the first number.

Let us write the equation as follows:

\[a + b = \dfrac{{23}}{{20}}a{\text{ }}..........(1)\]

Now let us simplify this further to obtain the relationship between the two numbers, \[a\] and \[b\] .

In equation (1), taking \[a\]in the left-hand side of the equation to the right-hand side, we get

\[b = \dfrac{{23}}{{20}}a - a\]

Taking \[a\] as a common term and solving, we get:

\[b = \left( {\dfrac{{23}}{{20}} - 1} \right)a\]

\[b = \left( {\dfrac{{23 - 20}}{{20}}} \right)a\]

\[b = \dfrac{3}{{20}}a{\text{ }}..........{\text{(2)}}\]

Hence, we obtained a relation between \[a\] and \[b\] .

To determine what percentage of the first number is the second number, we need to divide the second number by the first number and multiply the result by 100. This comes from the basic percentage formula as follows:

\[{\text{Percentage}} = \dfrac{{{\text{Required Value}}}}{{{\text{Total Value}}}} \times 100{\text{ \% }}\]

Here, the required value is the second number \[b\] and the total value is the first number \[a\] .

The required formula is as follows:

\[{\text{Percentage}} = \dfrac{b}{a} \times 100{\text{ \% }}...........{\text{(3)}}\]

Substituting equation (2) in equation (3), we get:

\[{\text{Percentage}} = \dfrac{{\dfrac{3}{{20}}a}}{a} \times 100{\text{ \% }}\]

Cancelling \[a\] in the numerator and denominator, we get:

\[{\text{Percentage}} = \dfrac{3}{{20}} \times 100{\text{ }}\% \]

Simplifying further we obtain:

\[{\text{Percentage}} = \dfrac{{300}}{{20}}{\text{ \% }}\]

\[{\text{Percentage}} = 15{\text{ \% }}\]

Hence, the correct answer is option (c).

Note: A common mistake committed is writing the equation as \[a + b = \dfrac{{23}}{{20}}b\] with \[b\] being the second number, which is wrong. You can also proceed by finding the ratio \[\dfrac{b}{a}\] directly from the equation \[b = \dfrac{3}{{20}}a{\text{ }}\] and multiplying the result by 100 to get the final answer.

Recently Updated Pages

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

What was the Metternich system and how did it provide class 11 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What organs are located on the left side of your body class 11 biology CBSE

What is pollution? How many types of pollution? Define it