Question

12. An article is sold at a profit of 10%. Had it been sold for 30 more, the profit would
have been 25%, find the C.P.​

Answer 1

Answer:

cp =rs 200

Step-by-step explanation:

11x/10+30=5x/4 or x=200

Answer 2

$\begin{gathered}\\\large{\underline{\underline{\sf{\pmb{Question:}}}}}\end{gathered}$

An article is sold at a profit of 10%. Had it been sold for 30 more, the profit would have been 25%, find the C.P.

$\begin{gathered}\\\large{\underline{\underline{\sf{\pmb{Required \: Answer:}}}}}\end{gathered}$

$\begin{gathered} \\ \underline{\underline{\sf{\pmb{Given:}}}}\end{gathered}$

$\begin{gathered}\\\sf{\rightarrow{The \: article \: is \: sold \: at \: a \: profit \: of \: 10\%}}\end{gathered}$

$\sf{\rightarrow{It \: would \: have \: been \: a \: profit \: of \: 25\% \: if \: it \: had \: been \: sold \: for \: 30 \: more.}}$

$\begin{gathered} \\ \underline{\underline{\sf{\pmb{To \: Find:}}}}\end{gathered}$

$\begin{gathered} \\ \sf{\rightarrow{The \: cost \: price \: of\: the \: article.}}\end{gathered}$

$\begin{gathered} \\ \underline{\underline{\sf{\pmb{Solution:}}}}\\\end{gathered}$

Let us assume that , the cost price of the article is x

Now, let's take a careful look at the question. We are told that the article was sold at a gain of 10% . Which means the gain was 10% on the cost price. Again, it would be gain of 25% if it had been sold for 30 more. This means, the difference of the sum of money between the gain of 10% and the gain of 25% is 30.

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Let's solve this!

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$\sf{In \: 10\% \: gain, \: the \: cost \: price \: is = \: \bold{x \times 10\% }}$

$\sf{\rightarrow{In \: 10\% \: gain, \: the \: cost \: price \: is = \: \bold{x \times \dfrac{10}{100} }}}$

$\begin{gathered} \sf{\rightarrow{In \: 10\% \: gain, \: the \: cost \: price \: is = \: \bold{ \dfrac{10x}{100}} \blue{ - - - - - - - - - - - (1)} }}\\\end{gathered}$

Again,

If the gain was 25%,

$\sf{In \: 25\% \: gain, \: the \: cost \: price \: is = \: \bold{x \times 25\% }}$

$\sf{\rightarrow{In \: 25\% \: gain, \: the \: cost \: price \: is = \: \bold{x \times \dfrac{25}{100} }}}$

$\begin{gathered} \sf{\rightarrow{In \: 25\% \: gain, \: the \: cost \: price \: is = \: \bold{ \dfrac{25x}{100} \blue{ - - - - - - - - - - (2)}}}}\\\end{gathered}$

From equation 1 and 2 , we can write:-

$\bold{\tt{ \dfrac{25x}{100} - \dfrac{10x}{100} = 30}}$

$\begin{gathered}\\\implies{\tt{ \dfrac{25x - 10x}{100} = 30}}\end{gathered}$

$\begin{gathered} \\ \implies{\tt{25x - 10x = 3000}} \: \: \: \: \: \: \boxed{\rm{Multiplying \: both \: sides \: by \: 100}}\end{gathered}$

$\begin{gathered}\\\implies{\tt{15x = 3000}}\end{gathered}$

$\begin{gathered} \\ \implies{\tt{x = \dfrac{3000}{15} }} \: \: \: \: \: \: \: \boxed{\rm{Dividing \: both \: sides \: by \: 15}}\end{gathered}$

$\begin{gathered} \\ \tt{\therefore{\bold{x = \red{200}}}}\end{gathered}$

$\begin{gathered} \\ \\ \underline{\boxed{\sf{Hence, \: the \: cost \: price \: of \: the \: article \: is \: \bold{\green{200}\checkmark{}}}}}\end{gathered}$