Question

A shopkeeper’s price is 50% above the cost price. If he allows his customer a discount of 30% what profit does he make?
A.15%
B.10%
C.5%
D.20%

Answer 1

Hint: In this question. A shopkeeper’s price is 50% above the cost price. From this we can easily find our marked Price. After we get the Marked Price then we can find the discount on the market Price (IMPORTANT NOTE: Discount is always given on marked price not on Cost Price). Then We can find Selling Price. Selling Price = Market price – Discount. Then we can find gain by subtracting Cost Price from Selling Price – Gain = SP – CP and Gain% = $\dfrac{{Gain}}{{C.p}} \times 100$. Let’s see how we can solve it.

Complete step-by-step answer:
Let the cost price be X Rupees.
Market price is 50% above the cost price.
So, Market price is X + 50% of X
We have,
Market Price = X + 50% of X
Market Price = $X + \dfrac{{50 \times X}}{{100}}$= $ = X + \dfrac{X}{2}$= $\dfrac{{2X + X}}{2} = \dfrac{{3X}}{2}$
Now, he allows his customer a discount of 30% on Market Price.
Discount = 30% on Market price
Discount = $\dfrac{{30}}{{100}} \times \dfrac{{3X}}{2}$= $\dfrac{{9X}}{{20}}$
Now, Selling price = Market Price - Discount
Selling Price = $\dfrac{{3X}}{2} - \dfrac{{9X}}{{20}}$= $ = \dfrac{{30X - 9X}}{{20}} = \dfrac{{21X}}{{20}}$
Gain = Selling price – cost price
Gain = $\dfrac{{21X}}{{20}} - X$= $\dfrac{{21X - 20X}}{{20}} = \dfrac{X}{{20}}$
Now, we will find Gain% = $\dfrac{{Gain}}{{C.p}} \times 100$
$
   \Rightarrow \dfrac{X}{{\dfrac{{20}}{X}}} \times 100 \\
   \Rightarrow \dfrac{X}{{20}} \times \dfrac{1}{X} \times 100 \\
   \Rightarrow 5\% \\
$
Option C is the correct option.

Note: You can solve this question with different methods also.
Let’s see how can we solve it:
Let,
CP = 100
MP = 50% of CP = 150
Discount = 30 %
Discount = 30% of MP = 30% of 150 = $\dfrac{{30}}{{100}} \times 150 = 45$
Selling Price = MP – Discount = 150 – 45 = 105
Gain = SP – CP = 105 – 100 = 5
Gain% = $\dfrac{{gain}}{{CP}} \times 100 = \dfrac{5}{{100}}$X 100 = 5% (Ans.)
Here we have used different formulas of profit and loss.
Profit or Gain = Selling price – Cost Price
Loss = Cost Price – Selling Price
 Profit percentage = (Profit /Cost Price) x 100
Loss percentage = (Loss / Cost price) x 100
Discount = Marked Price – Selling Price