Textile Engineering > GATE 2021 > Profit and Loss
Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost (Profit % = (Selling price - Cost) / Cost × 100). What is the discount on item Q, as a percentage of its marked price?
A
25
B
12.5
C
10
D
5

Correct : c

Item P: Cost = ₹5,400, Marked Price = ₹5,860, Profit% = ---
Item Q: Cost = ---, Profit% = 25, Marked Price = ₹10,000
Ratio of Cost of P to Cost of Q = 3:4
Step 1: Find Cost of Item Q
Cost of P ÷ Cost of Q = 3 ÷ 4
5,400 ÷ Cost of Q = 3 ÷ 4
Cost of Q = 5,400 × 4 ÷ 3
Cost of Q = ₹7,200
Step 2: Find Selling Price of Item Q
Profit% = (SP − Cost) ÷ Cost × 100
25 = (SP − 7,200) ÷ 7,200 × 100
SP − 7,200 = 25 × 7,200 ÷ 100
SP − 7,200 = 1,800
SP = 7,200 + 1,800
SP of Q = ₹9,000
Step 3: Find Discount on Item Q
Discount = Marked Price − Selling Price
Discount = 10,000 − 9,000
Discount = ₹1,000
Step 4: Find Discount as % of Marked Price
Discount% = (Discount ÷ Marked Price) × 100
Discount% = (1,000 ÷ 10,000) × 100
Discount% = 10%
The discount on item Q as a percentage of its marked price = 10% (Option C)

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