Question

Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is

• A. 20
• B. 25
• C. 15
• D. 10

Answer 1

The Correct Option is D

Let the cost price of the product be Rs \( x \). Gopi marks the price to achieve a 20% profit, hence the marked price \( M \) is:

\( M = x + 0.2x = 1.2x \) 

Ravi receives a 10% discount on the marked price, so the selling price \( S \) is:

\( S = M - 0.1M = 0.9M = 0.9 \times 1.2x = 1.08x \)

Ravi saves Rs 15 with this discount, therefore:

\( 0.1M = 15 \)

Substitute for \( M \):

\( 0.1 \times 1.2x = 15 \)

\( 0.12x = 15 \)

Solve for \( x \) (the cost price):

\( x = \frac{15}{0.12} = 125 \)

Thus, the selling price \( S \) is:

\( S = 1.08 \times 125 = 135 \)

The profit made by Gopi is the difference between the selling price and the cost price:

\( \text{Profit} = S - x = 135 - 125 = 10 \)

Therefore, the profit made by Gopi when selling the product to Ravi is Rs 10.

Answer 2

Let the cost price of the product be $C$ and the marked price be $M$.

Step 1: Expressing the Cost Price and Marked Price - Since Gopi wants to make a 20% profit,
\[ M = C \times 1.20 \]

Step 2: Discounted Price for Ravi - Ravi receives a 10% discount.
Price paid by Ravi $= M \times (1 - 0.10) = 0.90 \times M$
We are told that Ravi saves Rs 15, which means the discount amount is Rs 15:
Discount $= M \times 0.10 = 15$
Thus, the marked price is:
\[ M = \frac{15}{0.10} = 150 \]

Step 3: Calculate the Cost Price and Gopi's Profit From $M = C \times 1.20$, we can solve for the cost price:
\[ 150 = C \times 1.20 \implies C = \frac{150}{1.20} = 125 \]

Now, Gopi sells the product to Ravi for $0.90 \times 150 = 135$, so the profit Gopi makes is:
\[ Profit = 135 - 125 = 10 \]
Thus, the profit made by Gopi is Rs 10.