Question

(i) The cost of almirah is Rs. 2000. A gain of 10% should be made after a discount of 20%. Find the marked price.
(ii) A shopkeeper allows the discount of 10% on the goods and still makes 20% profit. Find the cost price of item whose M.P is 1700Rs/-

Answer 1

Hint:For part (i) and (ii) we follow same method of solving that is
Marked price (M.P) is the price that we show to the customer so the discount is applied to marked price only. So apply discount to marked price (M.P) we get selling price (S.P). The next cost price (C.P) is the price that we used to buy that product. So gain percentage is applied to it so that we get selling price. The applying of discount and gain percentage to specific parameters leads to the selling price that should be equal. So equating both selling prices we get the required to answer.

Complete step by step answer:
Let us solve question (i) first
Let us consider that
Cost price of almirah C.P = 2000Rs/-
Gain percentage = 10%
Discount = 20%
Let the marked price, M.P = \[x\]
Applying 20% discount to M.P, we get
 \[\begin{align}
  & P=x-\dfrac{20}{100}x \\
 & \Rightarrow P=\dfrac{8x}{10} \\
\end{align}\]
Taking cost price and applying the gain percentage we get
Total price after 10% gain in cost price,
\[\begin{align}
  & T=2000+2000\left( \dfrac{10}{100} \right) \\
 & \Rightarrow T=2000+200 \\
 & \Rightarrow T=2200 \\
\end{align}\]
Here, both values of ‘P’ and ‘T’ are selling prices of the almirah
Since both are selling prices they have to be equal. By equating ‘P’ and ‘T’ we get
\[\begin{align}
  & \Rightarrow T=P \\
 & \Rightarrow \dfrac{8x}{10}=2200 \\
 & \Rightarrow x=\dfrac{2200 \times 10}{8} \\
 & \Rightarrow x=2750 \\
\end{align}\]
Therefore, the marked price of the almirah is 2750Rs/-

Now, let us solve question (ii)
Let us consider that
Cost price of item C.P = \[x\]
Gain percentage = 20%
Discount = 10%
Let the marked price, M.P = 1700Rs/-
Applying 10% discount to M.P, we get
\[\begin{align}
  & \Rightarrow P=1700-1700\left( \dfrac{10}{100} \right) \\
 & \Rightarrow P=1700-170 \\
 & \Rightarrow P=1530 \\
\end{align}\]
Taking cost price and applying the gain percentage we get
Total price after 10% gain in cost price,
\[\begin{align}
  & \Rightarrow T=x+\dfrac{20}{100}x \\
 & \Rightarrow T=x+\dfrac{2}{10}x \\
 & \Rightarrow T=\dfrac{12x}{10} \\
\end{align}\]
Here, both values of ‘P’ and ‘T’ are selling prices of the item
Since both are selling prices they have to be equal. By equating ‘P’ and ‘T’ we get
\[\begin{align}
  & \Rightarrow T=P \\
 & \Rightarrow 1530=\dfrac{12x}{10} \\
 & \Rightarrow x=\dfrac{1530 \times 10}{12} \\
 & \Rightarrow x=1275 \\
\end{align}\]
Therefore the value of cost price of the item is 1275Rs/-

Note:
Either for part (i) or part (ii) you need to be very careful when it comes to the application of gain percentage and discount percentage to the parameters. Whatever you apply to gain and discount percentages it always leads to the selling price that will make you clear the differences between all the parameters. Students make mistakes while applying gain percentage and discount to marked price and cost price. Take care to which parameter gain and discount need to be applied.
The discount is for marked price and gives selling price.
The gain percentage is for cost price and gives selling price.