Question

Find a number whose fifth part is increased by 30 is equal to its fourth part decreased by 30.

Answer 1

Hint: in this the number is to be assumed and its one fifth part increased by thirty must be equated to its one fourth part decreased by 30.

Complete step-by-step answer:
Let the number be $x$ .
One fifth part of number, $n = \dfrac{1}{5}x$
One fourth of a number, $m = \dfrac{1}{4}x$

According to condition of the question,
Fifth part increased by 30 is equal to fourth part decreased by 30
$n + 30 = m - 30......(1)$

Substituting the value of $n$ and $m$ in equation (1),
$
  \dfrac{1}{5}x + 30 = \dfrac{1}{4}x - 30 \\
  \dfrac{1}{4}x - \dfrac{1}{5}x = 60 \\
  \dfrac{{5x - 4x}}{{20}} = 60 \\
  \dfrac{x}{{20}} = 60 \\
  x = 1200 \\
 $

Hence, the number is 1200
We can also verify this answer obtained by substituting the value back in the equation

Note: Calculation should be performed carefully and number obtained should be cross checked for accuracy.
For instance, $x = 1200$ , substitute it into equation(2) and equality should be satisfied.
$
  \dfrac{1}{5}\left( {1200} \right) + 30 = \dfrac{1}{4}\left( {1200} \right) - 30 \\
  270 = 270 \\
 $
Hence, our answer is correct.