Types of Discount Questions
In this article, we are going to have a look at the various kinds of questions formed on Discount.
Type 1: Discount percent and Profit/Loss percent given
Q. A shopkeeper is selling his goods at 40% discount, but still able to make 20% profit. Marked price is how much percent more than the cost price?
(a) 60% (b) 40% (c) 80% (d) 100%
Explanations :
Let cost price be Rs. 100 and mark up percentage be m%
So, price after mark-up = Rs. (100 + m)
Now, price after 40% discount = (100 + m) × (100 - 40)/100 = Rs. 0.6 (100 + m)
This is equal to 20% profit over cost price = 100 + 20% of 100 = 100 + 20 = Rs. 120 (because cost price = Rs. 100)
Equating both the terms, we get:
0.6 (100 + m) = 120
Or m = 100%
Applying formula of successive percentage increase, we get:
Net increase/decrease percentage = a + b + ab/100
Let a = m% (mark-up) and b = -40% (negative sign because it’s a discount)
We already know that Total profit = 20%
So, (m – 40) - 40m/100 = 20
Or m = 100%
Let Marked price be Rs. 100
As discount is 40%, so selling price (S.P.) = 100 - 40% of 100 = 100 - 40 = Rs. 60
Now, we know that profit = 20%
So, S.P. = 1.2 C.P.
or 60 = 1.2 C.P.
or C.P. = 60/1.2 = Rs. 50
So, Marked price is 100% more than the Cost price.
Q. A shopkeeper gives 50% discount on the market Price of a product and bears a loss of 40% as a result. If the product is sold at market Price only, then what will be the profit percentage?
(a) 10% (b) 20% (c) 16% (d) 18.33%
Explanation:
Let us assume the market price and cost price of that object to be Rs. 100 and Rs. x respectively.
Selling price of the object after discount = Rs. 50
After offering 50% discount the shopkeeper suffered a loss of 40%.
Loss percentage = [(CP - SP)/CP] × 100 = [(x - 50)/x] × 100 = 40
or 10x – 500 = 4x
or 6x = 500
x = 500/6 = Rs. 83.33
Hence, if sold at the market Price, the profit percentage = [(SP - CP)/CP] × 100 = [(100 - 83.33)/83.33] × 100 = 20%.
Answer: (b)
Q. The marked price and the cost price of a product are in the ratio 5 : 4. The shopkeeper makes a profit even by selling it on a discounted price. The profit percentage and the discount percentage were in the ratio 5 : 4. What is the profit percentage?
(a) 10% (b) 16.67% (c) 15% (d) 12.5%
Explanation:
Let the marked price be Rs. 5x, then cost price = Rs. 4x
Similarly, let the profit percentage and the discount percentage be 5y% and 4y% respectively.
Discount is given on the Marked price.
Selling Price = Marked price – Discount = 5x – (4y × 5x)/100 = 5x (1 – 4y/100) …(i)
Profit is counted on the Cost price.
Selling price = Cost price + profit = 4x + (5y × 4x)/100 = 4x (1 + 5y/100) …(ii)
Equating equations (i) and (ii), we get:
5x (1 – 4y/100) = 4x (1 + 5y/100)
or y = 100/40 = 5/2.
Now, profit percentage = 5y% = 25/2% = 12.5%
Answer: (d)
Type 2: Difference between two Discount percentages given
Q. While selling a pen, a shopkeeper gives a discount of 6%. If he had given a discount of 8%, he would have got Rs. 12 less as profit. What must be the marked price of the pen?
(a) Rs. 500 (b) Rs. 600 (c) Rs. 700 (d) Rs. 750
Explanation:
Let the marked price of the pen be Rs. p.
Difference of discounts = (8 - 6)% = 2%
2% of p = 12
or (2/100) p = 12
or p = (12 × 100)/2
or p = Rs. 600
Answer: (b)