Question

A firm, dealing in furniture, allows 4% discount on the marked price of each item. What price must be marked on a dining table which costs Rs.400 to assemble, so as to make a profit of 20%?

Answer 1

Hint: Let the marked price be x. The discount price is 4% on x which is 0.04x. Selling price (SP) is marked price minus discount price. Find the selling price. Substitute the values of SP, CP and profit in the below formula and solve for the value of x.
Formula used:
 $ Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 $ , where SP is the selling price and CP is the cost price.

Complete step-by-step answer:
We are given that a firm, dealing in furniture, allows 4% discount on the marked price of each item.
We have to find the marked price of a dining table whose cost is Rs. 400 and should make profit 20%.
Let the marked price (MP) of the dining table is x.
Discount is 4% of marked price, which is $ D = \dfrac{4}{{100}}x = 0.04x $
We know that the selling price is marked price minus discount price.
 $
  SP = MP - D \\
  MP = x,D = 0.04x \\
  \Rightarrow SP = x - 0.04x = 0.96x \\
  $
The cost price (CP) of the dining table is Rs. 400 and profit by selling it is 20%.
Substituting the values of SP, CP and profit we get
 $
  Profit = \dfrac{{\left( {SP - CP} \right)}}{{CP}} \times 100 \\
  SP = 0.96x,CP = 400,Profit = 20 \\
  \Rightarrow 20 = \dfrac{{0.96x - 400}}{{400}} \times 100 \\
  \Rightarrow 20 = \dfrac{{0.96x - 400}}{4} \\
  \Rightarrow 0.96x - 400 = 80 \\
  \Rightarrow 0.96x = 480 \\
  \Rightarrow x = \dfrac{{480}}{{0.96}} \\
  \therefore x = Rs.500 \\
 $
The value of x which is the marked rice is Rs. 500.
Therefore, the cost price of dining table is Rs. 400, the marked price is Rs. 500 and the discount is 4% which is Rs. 20 and the selling price 500-20= Rs. 480.

Note: Cost price is the price at which an item is purchased and the selling price is the price at which that item is sold. The actual selling price will be marked price minus discount price, when there is any discount. If there is no discount then the marked price is the actual selling price.