Question

After allowing a discount of \[7\dfrac{1}{2}\% \] on the marked price, a toy was sold for Rs.\[555\]. Find its marked price.

Answer 1

Hint: Let us consider, the price of an object is \[Rs.{\text{ }}a\], and the percentage of discount \[b\% \] then after the discount the price of the object is Rs. \[a \times \dfrac{{100 - b}}{{100}}\]. With the help of this we will mark the marked price.

Complete step-by-step answer:
It is given that after allowing a discount of \[7\dfrac{1}{2}\% \] on the marked price, a toy was sold for Rs.\[555\].
Let us consider, the marked price of the toy is \[x\].
It is given that the percentage of discount on marked price is \[7\dfrac{1}{2}\% \].
That is $\dfrac{{15}}{2}\% $ percentage is discounted from market price.
Converting the percentage to fraction form by dividing 100 to the percentage value.
Using percentage formula we can write the$\dfrac{{15}}{2}\% $percentage as $\dfrac{{15}}{{200}}$
From this we can find the price that is being discounted from the marked price,
Hence the amount of discount is \[x \times \dfrac{{15}}{{200}} = \dfrac{{15x}}{{200}}\]
After the discount, the price of the toy is found by subtracting the price for which the toy is sold and the amount discounted that is,
The price of the toy is\[ = x - \dfrac{{15x}}{{200}} = \dfrac{{185x}}{{200}}\]
The selling price of the toy is Rs.\[555\].
 According to the problem, we can equate the prices therefore we get,
\[\dfrac{{185x}}{{200}} = 555\]
Let us solve the above equation, we get,
\[x = 555 \times \dfrac{{200}}{{185}} = 600\]
Hence, the marked price of the toy is Rs \[600\].

Note: The discount refers to an amount or percentage deducted from the selling price. After the discount, the price will be reduced.
The sum can be solved by another process.
The marked price will be \[ = Rs.555 \times \dfrac{{100}}{{100 - \dfrac{{15}}{2}}}\]
By simplifying we get,
The marked price is Rs. \[600\]