Question

5. Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5.​

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Assume the number be p.

★Hence we have :-

${\boxed{\sf\:{5th part=\dfrac{p}{5}}}}$

${\boxed{\sf\:{4th part=\dfrac{p}{4}}}}$

★Condition is like that :-

${\boxed{\sf\:{\dfrac{p}{5}+5=\dfrac{p}{4}-5}}}$

Solving the denominator we get :-

${\boxed{\sf\:{\dfrac{p+25}{5}=\dfrac{p-20}{4}}}$

★Now by cross multiply we get :-

4(p + 25) = 5(p - 20)

4p + 100 = 5p - 100

5p - 4p = 200

★Therefore we get,

p = 200

Answer 2

$\huge\star\underline\mathfrak\pink{Answer}$

$\huge\boxed{Number\:=\:200}$

_____________________

$\huge\star\underline\mathfrak\pink{Explanation}$

Let the number be n.

Fifth part of the number be n/5.

fourth part of the number be n/4.

_____________________

According to question,

$(\frac{n}{5} + 5) = ( \frac{n}{4} - 5)$

Now, after taking LCM,

$\frac{n + 25}{5} = \frac{n - 20}{4}$

By cross multiplying,

$4(n + 25) = 5(n - 20)$

$4n + 100= 5n - 100$

$4n - 5n = - 100 - 100$

$- n = - 200$

$n = 200$

Therefore, the number is 200.