A pen costs ₹121.5 and its marked price is ₹150. What should be two equal successive percentage discounts on marked price to have no profit or loss?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 10%.
Let each successive discount be x%
The cost price (CP) of the pen is ₹121.5
The marked price (MP) of the pen is ₹150
After two successive discounts of x%, the selling price (SP) should be equal to the CP, which means no profit or loss.
Therefore, we can set up two equations:
Selling price after two discounts: SP = MP × (1 - x/100)2
Selling price equals cost price: SP = CP = ₹121.5
Substituting equation 1 into equation 2, we get:
⇒ ₹121.5 = ₹150 × (1 - x/100)2
Simplifying the equation:
⇒ 0.81 = (1 - x/100)2
Taking the square root of both sides:
⇒ 0.9 = 1 - x/100
⇒ x/100 = 0.1
⇒ x = 10%
Therefore, each successive discount should be 10% to achieve no profit or loss