Question

A dealer of scientific instruments allows a 20% discount on the marked price of the instrument and still makes a profit of 25%. If his gain over the sale of an instrument is Rs. 150 find the marked price of the instrument.

Answer 1

Hint: We can make equations for various prices using variables. We have been given the profit percentage and profit amount and equating the two, we can find the value of variables which can be substituted in the equations for different prices. Using these equations and respective formulas, we can find the required value of marked price.
Formulas to be used:
Profit = P% of CP
SP = CP + P
SP = MP – D
 $ D\% = \dfrac{D}{{MP}} \times 100 $
Where, CP, MP and SP are cost, selling and marked prices respectively. D is a discount and P is a profit.

Complete step-by-step answer:
It is given that the dealer gains Rs. 150 after allowing a discount of 20% on the marked price (MP) and his percentage of profit is 25%.
Let the cost at which he bought the instrument be Rs. x
🡪 CP = Rs. x and MP = Rs. y.
Profit is given by the product of profit percentage and cost price:
Profit = 25% of CP
           = 25% of x
\[
  \Rightarrow P = 25\% x = \dfrac{{25}}{{100}}x \\
   \Rightarrow P = 0.25x \;
 \]
Selling price (SP) of the instrument is given by the sum of CP and profit:
SP = CP + P
\[
  \Rightarrow SP = x + 0.25x \\
   \Rightarrow SP = 1.25x \;
 \]
Now, profit price is Rs. 150 and profit percentage is 25%.
P = 150
\[
  \Rightarrow 0.25x = 150 \\
  \Rightarrow x = \dfrac{{150}}{{0.25}} \\
  \Rightarrow x = 150 \times 4 \\
   \Rightarrow x = 600 \;
 \]
We have the cost price as x , so the cost price of the instrument is Rs. 600
The value of SP is 1.25 x so the SP of the instrument is:
 $ 1.25 \times 600 = 750 $
Selling price of the instrument is also equal to the difference between marked price (MP) and discount (D).
🡪 SP = MP – D _____ (1)
Now, discount percentage (D%) is given as:
 $ D\% = \dfrac{D}{{MP}} \times 100 $ here,
Discount percentage (D%) = 20 (given)
MP = y (let)
 $
   \Rightarrow 20\% = \dfrac{D}{y} \times 100 \\
   \Rightarrow D = \dfrac{{y \times 20}}{{100}} \\
   \Rightarrow D = 0.2y \;
  $
Substituting the known value in (1), we get:
\[
  750 = {\text{ }}y-0.2y \\
  \Rightarrow 0.8y = 750 \\
  \Rightarrow y = \dfrac{{750 \times 10}}{8} \\
  y = 437.5 \;
 \]
Therefore, find the marked price of the instrument is Rs. 437.5

Note: We can convert the fractions into decimals or vice – versa according to our needs. Here the calculations were easier in the decimal form so we converted the fractions into decimals. For the conversions we can keep in mind that the number of zeroes in the fraction will be equal to the number of digits after the decimal.