Question

The cost price of a printer is Rs. 3400, which is \[15\% \] below the marked price. If the article is sold at a discount of \[10\% \], find
(a) the marked price
(b) the selling price
(c) the profit
(d) the profit percentage.

Answer 1

Hint:
Here, we need to find the marked price, selling price, profit, and profit percentage. We will use the cost price and its given relation with the marked price to find the marked price. We will use the marked price and discount to calculate the selling price using the formula. We will use the selling price and cost price to find the profit. Finally, we will substitute the profit and cost price in the formula and find the profit percentage.

Formula Used:
We will use the following formulas:
1) \[S.P. = M.P. - {\rm{Discount}}\], where \[S.P.\] is the selling price of the object and \[M.P.\] is the marked price of the object
2) \[{\rm{Profit}} = S.P. - C.P.\], where \[C.P.\] is the cost price of the object and \[S.P.\] is the selling price of the object.
3) The profit percent is given by \[{\rm{Profit Percent}} = \dfrac{{{\rm{Profit}}}}{{C.P.}} \times 100\], where \[C.P.\] is the cost price of the object.

Complete Step by Step Solution:
(a)
Let the marked price be Rs. \[x\].
It is given that the cost price is \[15\% \] below the marked price.
Therefore, we get
\[C.P. = M.P. - 15\% \] of \[M.P.\]
Substituting \[M.P. = x\] in the above equation, we get
\[ \Rightarrow C.P. = x - 15\% \] of \[x\]
Rewriting the expression, we get
\[ \Rightarrow C.P. = x - \dfrac{{15}}{{100}} \times x\]
It is given that the cost price is Rs. 3400.
Therefore, we get
\[ \Rightarrow 3400 = x - \dfrac{{15}}{{100}} \times x\]
\[ \Rightarrow 3400 = x - \dfrac{{15x}}{{100}}\]
This is a linear equation in one variable. We will solve this to find the value of \[x\].
Subtracting the terms by taking L.C.M., we get
\[\begin{array}{l} \Rightarrow 3400 = \dfrac{{100x - 15x}}{{100}}\\ \Rightarrow 3400 = \dfrac{{85x}}{{100}}\end{array}\]
Multiplying both sides of the equation by 100, we get
\[ \Rightarrow 340000 = 85x\]
Dividing both sides of the equation by 85, we get
\[ \Rightarrow x = 4000\]
Therefore, we get the marked price as Rs. 4000.
(b)
Now, the discount of \[10\% \] is on the marked price.
We can find the discount by multiplying the discount percentage with the marked price.
Thus, we get
\[{\rm{Discount}} = 10\% \] of \[M.P.\]
\[ \Rightarrow {\rm{Discount}} = 10\% \] of 4000
\[ \Rightarrow {\rm{Discount}} = \dfrac{{10}}{{100}} \times 4000\]
Multiplying the terms, we get
\[ \Rightarrow {\rm{Discount}} = 400\]
\[\] We get the discount as Rs. 400.
The difference of the marked price and the discount is the selling price.
Substituting Rs. 4000 for marked price and Rs. 400 for discount in the formula \[S.P. = M.P. - {\rm{Discount}}\], we get
\[ \Rightarrow {\rm{SP}} = 4000 - 400 = 3600\]
Therefore, the selling price is Rs. 3600.
(c)
The profit is the difference in the selling price and cost price.
Substituting Rs. 3400 for cost price and Rs. 3600 for selling price in the formula \[{\rm{Profit}} = S.P. - C.P.\], we get the profit as
\[ \Rightarrow {\rm{Profit}} = 3600 - 3400\]
\[\therefore \text{Profit}=200\]
Therefore, we get the profit as Rs. 200.
(d)
We will now find the profit percent.
Substituting the profit as Rs. 200 and the cost price as Rs. 3400 in the formula \[{\rm{Profit Percent}} = \dfrac{{{\rm{Profit}}}}{{C.P.}} \times 100\], we get
\[{\rm{Profit Percent}} = \dfrac{{200}}{{3400}} \times 100\]
Simplifying the expression, we get
\[\begin{array}{l} \Rightarrow {\rm{Profit Percent}} = \dfrac{{100}}{{17}}\\ \Rightarrow {\rm{Profit Percent}} = 5.88\% \end{array}\]

\[\therefore \] We get the profit percent as \[5.88\% \].

Note:
We have formed a linear equation in one variable in terms of \[x\] in the solution. A linear equation in one variable is an equation of the form \[ax + b = 0\], where \[a\] and \[b\] are integers. A linear equation of the form \[ax + b = 0\] has only one solution.
A common mistake is to assume the selling price and marked price to be the same. The terms ‘selling price’ and ‘marked price’ are not the same.
The selling price is the price at which an object is sold. It is the price which the customer pays.
The marked price is the listed price at which an object is intended to be sold.