Question

If the selling price of an article is five times the discount offered and if the percentage of discount is equal to the percentage profit, what is the ratio of the discount offered to the cost price?

• A. 11:30
• B. 4:15
• C. 7:30
• D. 1:6
• E. 3:25

Answer 1

The Correct Option is C

The correct answer is option (C): 7:30

Let's break down the problem step-by-step to show why the ratio D : CP = 7 : 30.

Define symbols

• SP = Selling Price
• D = Discount (absolute amount)
• MP = Marked Price
• CP = Cost Price
• P = Profit (absolute amount)

Given

• SP = 5D (selling price is five times the discount)
• % Discount = % Profit

Relations

• SP = MP − D
• SP = CP + P
• % Discount = D / MP
• % Profit = P / CP

Step 1 — express MP and P using SP = 5D

From SP = MP − D and SP = 5D we get: 5D = MP − D ⇒ MP = 6D.

From SP = CP + P and SP = 5D we get: 5D = CP + P ⇒ P = 5D − CP.

Step 2 — use %Discount = %Profit

(D / MP) = (P / CP). Substitute MP = 6D to get:
D / (6D) = P / CP ⇒ 1/6 = P / CP ⇒ CP = 6P.

Step 3 — eliminate P

We have P = 5D − CP and CP = 6P. Substitute CP into the first:
P = 5D − 6P ⇒ 7P = 5D ⇒ P = (5/7)D. Then CP = 6P = 6 · (5/7)D = (30/7)D.

Step 4 — form the required ratio

D : CP = D : (30/7)D = 1 : (30/7) = 7 : 30.

Conclusion: The ratio of the discount to the cost price is 7 : 30, confirming option (C).