Question

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

Answer 1

Hint:
first, let the required number be $x$. Then use the given condition, which is four-fifth of a number is more than three-fourth of a number by 4. Find the number. Next, solve the equation to find the value of $x$.

Complete step by step solution:
Let the number be $x$.
We are given that the four-fifth of x is more than three-fourth of $x$
Then according to the given condition, we have the equation as,
\[\dfrac{{4x}}{5} = \dfrac{{3x}}{4} + 4\]
To solve the above equation, bring the terms containing $x$ on one side
\[\dfrac{{4x}}{5} - \dfrac{{3x}}{4} = 4\]
Take the LCM of 5 and 4 and the expression in the left-hand side of the above expression.
$
  \dfrac{{16x - 15x}}{{20}} = 4 \\
   \Rightarrow \dfrac{x}{{20}} = 4 \\
$
Multiply both sides by 20
$x = 4 \times {20} $

Hence, the required number is 80.

Note:
Formation of the equation should be correct. Also, we cannot add or subtract two unlike fractions directly. We will first convert unlike fraction into like fraction using LCM of the denominator and then add the terms.