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

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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.