Question

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

Answer 1

Answer:

79

Step-by-step explanation:

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Answer 2

$\large\sf\underline{Given\::}$

• A number whose fifth part increased by 5 is equal to its fourth part diminished [decreased] by 5.

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$\large\sf\underline{To\:find\::}$

• The number which would verify my given part.

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$\large\sf\underline{Assumption\::}$

So let us assume the number to be x.

Now :

• Fifth part of x = $\sf\:\frac{1}{5} \times x \:=\:\frac{x}{5}$

• Fourth part of x = $\sf\:\frac{1}{4} \times x \:=\:\frac{x}{4}$

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$\large\sf\underline{Solution\::}$

Let's form an equation from the statement provided to us :

$\sf\:★\:Fifth\:part\:of\:x+5\:=\:Fourth\:part\:of\:x-5$

• Substituting the values we have assumed

$\sf\implies\:\frac{x}{5}+5=\:\frac{x}{4}-5$

• Finding LCM of 5 and 1 in RHS 4 and 1 in LHS

$\sf\implies\:\frac{x+25}{5}\:=\:\frac{x-20}{4}$

• Cross multiplying

$\sf\implies\:4(x+25)\:=\:5(x-20)$

$\sf\implies\:4x+100\:=\:5x-100$

• Transposing 5x to the other side

$\sf\implies\:4x-5x+100\:=\:-100$

$\sf\implies\:-x+100\:=\:-100$

• Transposing 100 to the other side

$\sf\implies\:-x\:=\:-100-100$

$\sf\implies\:-x\:=\:-200$

$\sf\implies\:\cancel{-}x\:=\:\cancel{-}200$

$\large{\mathfrak\red{\implies\:x\:=\:200}}$

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‎ ______________________

$\large\sf\underline{Verifying\::}$

$\sf\implies\:\frac{x}{5}+5=\:\frac{x}{4}-5$

• Let's substitute the value of x as 200

$\sf\implies\:\frac{200}{5}+5=\:\frac{200}{4}-5$

$\sf\implies\:\frac{200+25}{5}\:=\:\frac{200-20}{4}$

$\sf\implies\:\frac{225}{5}\:=\:\frac{180}{4}$

• Cross multiplying

$\sf\implies\:225 \times 4\:=\:180 \times 5$

$\sf\implies\:900\:=\:900$

$\small\fbox\purple{※\:Hence\:Verified}$

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$\dag\:\underline{\sf Therefore\:required \:number\:is\:200.}$

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!! Hope it helps !!