Question

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

Answer 1

Answer:

The required number is 200.

Step-by-step-explanation:

Let the number be x.

Fifth part of number = $\displaystyle{\sf\:\dfrac{x}{5}}$

Fourth part of number = $\displaystyle{\sf\:\dfrac{x}{4}}$

From the given condition,

$\displaystyle{\sf\:\dfrac{x}{5}\:+\:5\:=\:\dfrac{x}{4}\:-\:5}$

$\displaystyle{\implies\sf\:\dfrac{x}{5}\:-\:\dfrac{x}{4}\:=\:-\:5\:-\:5}$

$\displaystyle{\implies\sf\:\dfrac{4x\:-\:5x}{20}\:=\:-\:10}$

$\displaystyle{\implies\sf\:\cancel{-}\:\dfrac{x}{20}\:=\:\cancel{-}\:10}$

$\displaystyle{\implies\sf\:x\:=\:10\:\times\:20}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:200\:}}}}$

∴ The required number is 200.

Answer 2

→ Given,

We have to find a number whose fifth part increased by 5 is equal to its fourth part diminished by 5.

→ Let us assumed that,

The number is = x

So,

$\pink{ \boxed{ \boxed{ \begin{array}{cc} \small{ \rm \to \: fifth \: part \: of \: the \: number \: = x \: of \: \frac{1}{5} = \frac{x}{5}} \\ \\ \small{ \rm \: and \: when \: it \: is \: incieased \:by \: 5 \: then \: it\: is \: = \frac{x}{5} + 5 } \end{array}}}}$

and

$\green{ \boxed{ \boxed{ \begin{array}{cc} \small{ \rm \to \: fourth\: part \: of \: the \: number \: = x \: of \: \frac{1}{4} = \frac{x}{4}} \\ \\ \small{ \rm \: and \: when \: it \: is \: diminished \:by \: 5 \: then \: it\: is \: = \frac{x}{4} - 5 } \end{array}}}}$

According to the question,

$\orange{ \boxed{ \boxed{ \begin{array}{cc} \rm \: \frac{x}{5} + 5 = \frac{x}{4} - 5 \\ \\ \rm \implies \: \frac{x}{4} - \frac{x}{5} = 5 + 5 \\ \\ \rm \implies \: \frac{5x - 4x}{20} = 10 \\ \\ \rm \implies \: x = 10 \times 20 \\ \\ \rm \implies \: x = 200\end{array}}}}$

So the number is = 200