Question

X + 12% of X = 15680 please give step by step explanation to find X sorry guys typed a wrong question...​

Answer 1

$\Large {\underline { \sf \orange{Clarification :}}}$

Here,we are given a question from the topics percentage and linear equations. We have to find the value of x in the given equation but we are also given a certain percent. So, first of all we'll convert the percent into fraction. After that, by using transposition method we'll solve the equation further and will find the value of x.

$\bf \red { \dag }$ Transposition method :

• This is the method used to solve a linear equation having variables and constants.
• In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.

$\Large {\underline { \sf \orange{Explication \: Of \: Steps :}}}$

According to the question,

$\longrightarrow \sf { x + 12 \% \: of \: x = 15680 }$

Conversion of percent into fraction :

We know that,

• x % means x hundredths, i.e $\sf {\dfrac{x}{100} }$

So,

$\longrightarrow \sf { 12 \: \% = \dfrac{12}{100} }$

Substituting values,

$\longrightarrow \sf { x + \dfrac{12}{100}\: of \: x = 15680 }$

$\longrightarrow \sf { x + \dfrac{12}{100}\times x = 15680 }$

$\longrightarrow \sf { x + \dfrac{12}{100} x = 15680 }$

$\longrightarrow \sf { \dfrac{100x + 12x}{100} = 15680 }$

$\longrightarrow \sf { \dfrac{112x}{100} = 15680 }$

$\longrightarrow \sf { 112x = 15680 \times 100 }$

$\longrightarrow \sf { 112x = 1568000 }$

$\longrightarrow \sf { x = \cancel{ \dfrac{1568000}{112} }}$

$\longrightarrow$ ❝ $\boxed{ \sf \orange { x = 14,000 }}$ ❞

Therefore, value of x is 14,000.

$\Large {\underline { \sf \orange{Verification :}}}$

Let's verify our solution by substituting the value of x in the equation and checking whether R.HS and L.H.S are equal or not.

• $\bf {L.H.S \: : }$

$\longrightarrow \sf { x + 12 \% \: of \: x }$

$\longrightarrow \sf { 14000 + \Bigg \lgroup \dfrac{12}{100} \times 14000 \Bigg \rgroup }$

$\longrightarrow \sf { 14000 + \lgroup 12 \times 140 \rgroup }$

$\longrightarrow \sf { 14000 + 1680 }$

$\longrightarrow \sf { 15680 }$ ★

• $\bf {R.H.S \: : }$

$\longrightarrow \sf { 15680 }$ ★

L.H.S = R.H.S , hence verified !