# Four fifth of a number is 4 more than three fourth of a number. Find the number.

Answer

Verified

206.1k+ views

**Hint:**In this question, we are given a statement of a number and we need to find the number. For this, we will first suppose the numbers as x. Then using the given statement, we will form an equation of x. Solving the equation will give us the value of x which is our required numbers. We will use x of y as $x\times y=xy$.

**Complete step-by-step solution**

Let us suppose that, the given number is x.

Now, we need to find the value of x using the given statement. Let us first find the form of the number which is being used in the statement. Four-fifths of a number means we need to find ${{\dfrac{4}{5}}^{th}}$ of numbers. Here, we have the supposed number as x. So we get $\dfrac{4}{5}\times x$.

Four fifth numbers $\Rightarrow \dfrac{4}{5}x$.

Similarly, three fourth of a number means we need to find ${{\dfrac{3}{4}}^{th}}$ of x which becomes equal to $\dfrac{3}{4}\times x$.

Hence, three fourth of the number $\Rightarrow \dfrac{3}{4}x$.

Now we are given that four-fifths of the number is 4 more than three-fourths of numbers. So we can say $\dfrac{4}{5}x$ is 4 more than $\dfrac{3}{4}x$.

In mathematical terms, we can write it as:

$\dfrac{4}{5}x=4+\dfrac{3}{4}x$.

Hence we have formed an equation in terms of x. Let us solve it to find the value of x.

Taking terms containing x on the left side of the equation, we get:

$\dfrac{4}{5}x-\dfrac{3}{4}x=4$.

Taking LCM of 20 on the left side of the equation, we get:

$\begin{align}

& \Rightarrow \dfrac{\left( 4\times 4 \right)x-\left( 3\times 5 \right)x}{20}=4 \\

& \Rightarrow \dfrac{16x-15x}{20}=4 \\

& \Rightarrow \dfrac{x}{20}=4 \\

\end{align}$.

Cross multiplying we get:

$\Rightarrow x=4\times 20=80$

Hence the value of x is 80.

**Since x was supposed to be the given number, so our required number is 80.**

**Note:**Students can check their answer by putting a value of 80 in the equation and checking if the left side is equal to the right side. Here we have taken LCM as 20 because 5 and 4 are coprime, so LCM will be $5\times 4=20$. Take care of signs while solving the equation.

Recently Updated Pages

Paulings electronegativity values for elements are class 11 chemistry CBSE

For a particle executing simple harmonic motion the class 11 physics CBSE

Does Nichrome have high resistance class 12 physics CBSE

The function f satisfies the functional equation 3fleft class 12 maths JEE_Main

Write a letter to the Principal of your school to plead class 10 english CBSE

Look at the handout below Write a letter to the organizers class 11 english CBSE

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?