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A seller allows a discount of $5\% $ on a watch. If he allows a discount of $7\% $, he earns Rs.$15$ less in the profit. What is the marked price?
A) $Rs.697.50$
B) $Rs.712.50$
C) $Rs.750$
D) $Rs.817.50$

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Last updated date: 20th Jun 2024
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Answer
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Hint: The price on the label of an article is called the marked price or list price. This is the price at which the product is intended to be sold. If $x$ be the profit that the seller makes on a 5% discount. Then,$\left( {x - 15} \right)$ is the profit that he makes on a 7% discount according to the question. Then the formed equation can be expressed as:
\[(100 - 5)\% {\text{ }}of{\text{ }}M.P - \left( {100 - 7} \right)\% {\text{ }}of{\text{ }}M.P = x - \left( {x - 15} \right) = 15\]

Complete step-by-step answer:
It is given to us that a seller allows a discount of 5% on a watch and it is also given that if he allows a discount of $7\% $, then he earns Rs.15 less in the profit.
We assume that the profit that the seller makes at a 5% discount will be $x$.
Then, according to the question, the profit that the seller makes on a $7\% $discount will be $(x - 15)$.
So, the formed equation to us is given as:
\[\left[ {(100 - 5)\% {\text{ }}of{\text{ }}M.P} \right] - \left[ {\left( {100 - 7} \right)\% {\text{ }}of{\text{ }}M.P} \right] = x - \left( {x - 15} \right) = 15\]
\[ \Rightarrow 2\% {\text{ }}of{\text{ }}M.P{\text{ }} = 15\]
Simplify the equation:
\[ \Rightarrow \dfrac{2}{{100}} \times M.P = 15\]
\[ \Rightarrow M.P = \dfrac{{1500}}{2}\]
\[ \Rightarrow M.P = 750\]
Hence, the Marked Price of the watch is Rs.750.

Therefore, the correct option is the option (C).

Note: An important aspect to notice and keep in mind is that Discount percent is calculated as a percentage of the market price. Considered the price tag on a shirt is $Rs.500$ and the discount being offered is 10%. If one were to purchase the shirt, the 10% discount will be calculated on the price tag i.e., $Rs.500$ in this case and one would pay the shopkeeper $Rs.450$
The value on the price tag is called Market price (M.P).