Question

If the certain dealer buys an article for Rs. \[380\]. Then, what will be the price that should be marked so that after allowing a discount of ‘\[5\% \]’ that still makes a profit of ‘\[25\% \]’ on the article?
A. Rs. \[250\]
B. Rs. \[750\]
C. Rs. \[500\]
D. None of these

Answer 1

Hint: Here, we will be using the concept of algebraic solution which resembles that first of all calculating a profit of ‘\[25\% \] i.e. \[\dfrac{{\left( {100 + 25} \right)}}{{100}} \times 380\]’ on Rs. \[380\] respectively and then (similarly) solving the further discount of Rs. \[5\% \] considering ‘x’ as the required price i.e. ‘\[\dfrac{{\left( {100 - 5} \right)}}{{100}} \times \left( x \right)\]’, which seems to be equal in condition. Hence, simplifying the equations, the desired value is obtained.

Complete step-by-step answer:
Since, we have given that
A certain dealer buys an article for Rs. \[380\],
Hence, Cost price i.e. (C.P.) of the product becomes
\[ \Rightarrow C.P. = 380\]
But, it is also given that
On selling the respective article, it makes the profit of ‘\[25\% \]’ i.e. on the C.P. that the dealer bought his respective article that is mathematically represented by,
\[ \Rightarrow S.P. = \dfrac{{\left( {100 + 25} \right)}}{{100}} \times \left( x \right)\]
\[ \Rightarrow S.P. = \dfrac{{125}}{{100}} \times 380\]
Hence, solving the equation, we get
\[ \Rightarrow S.P. = \dfrac{5}{4} \times 380\] … (i)
But, the given condition resembles that it seems the extra ‘\[5\% \]’ discount on the respective article
Mathematically, the equation seems that
\[ \Rightarrow S.P. = \dfrac{{\left( {100 - 5} \right)}}{{100}} \times \left( x \right)\]
Where, ‘\[x\]’ is the required selling price at discount ‘\[5\% \]’ after applying the ‘\[25\% \]’ profit.
\[ \Rightarrow S.P. = \dfrac{{95}}{{100}} \times \left( x \right)\] … (ii)
Hence, the condition (ii) equals to the equation (i), we get
\[ \Rightarrow \dfrac{{125}}{{100}} \times 380 = \dfrac{{95}}{{100}} \times \left( x \right)\]
\[ \Rightarrow 125 \times 380 = 95 \times \left( x \right)\]
Simplifying the equation algebraically, we get
\[ \Rightarrow x = \dfrac{{125 \times 380}}{{95}}\]
\[ \Rightarrow x = \dfrac{{47500}}{{95}}\]
Hence, the required selling price of the article that the dealer bought at Rs. \[380\] is
\[ \Rightarrow x = 500\] i.e.
\[ \Rightarrow S.P. = \]Rs. \[500\]
So, the correct answer is “Option C”.

Note: One must be able to remember the definition of percentage that is always calculated (or, divided) with respect to ‘\[100\]’. In case, also remember the formulae to calculate the profit or loss of the respective product, that is, ‘\[profit = \dfrac{{\left( {S.P.} \right) - \left( {C.P.} \right)}}{{100}}\]’, ‘\[loss = \dfrac{{\left( {C.P.} \right) - \left( {S.P.} \right)}}{{100}}\]’, ‘\[loss\% = \dfrac{{loss}}{{\left( {C.P.} \right)}}\]’, ‘\[profit\% = \dfrac{{profit}}{{\left( {S.P.} \right)}}\]’, so as to be sure of our final answer.