Question

If on a marked price, the difference of selling prices with a discount of 30% and two successive discounts of 20% and 10% is 72, then the marked price (in rupees) ?

• A. 3,600
• B. 3,000
• C. 2,500
• D. 2,400

Hint:

Always carefully calculate the effective discount for successive discounts ($d_1, d_2$): $d_{eff} = d_1 + d_2 - \frac{d_1 d_2}{100}$. Then use this to find the selling price. A single discount of $X\%$ means the selling price is $(100-X)\%$ of the marked price.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem involves calculating the marked price (MP) of an item, given the difference between two different discount schemes applied to it.

Step 2: Key Formula or Approach:
1. Let the Marked Price be MP.
2. Calculate the Selling Price (SP1) after a single discount of 30%.
3. Calculate the effective discount for two successive discounts of 20% and 10%.
4. Calculate the Selling Price (SP2) after the two successive discounts.
5. Use the given difference (SP1 - SP2) to find MP.

Step 3: Detailed Explanation:
Let the Marked Price (MP) be Rs. \( x \).
Scenario 1: Single discount of 30%
Discount = 30% of MP = $0.30x$.
Selling Price 1 (SP1) = MP - Discount = $x - 0.30x = 0.70x$.
Scenario 2: Two successive discounts of 20% and 10%
First discount = 20% on MP. Price after first discount = $x(1 - 0.20) = 0.80x$.
Second discount = 10% on the discounted price ($0.80x$).
Price after second discount = $0.80x (1 - 0.10) = 0.80x (0.90) = 0.72x$.
Selling Price 2 (SP2) = $0.72x$.
Alternatively, calculate effective discount for successive discounts $d_1, d_2$:
Effective Discount = $d_1 + d_2 - \frac{d_1 d_2}{100} = 20 + 10 - \frac{20 \times 10}{100} = 30 - 2 = 28\%$.
So, SP2 = MP - (28% of MP) = $x - 0.28x = 0.72x$.
Given Difference:
The difference between the two selling prices is Rs. 72.
\[ \text{SP1} - \text{SP2} = 72 \]
\[ 0.70x - 0.72x = 72 \]
\[ -0.02x = 72 \]
\[ 0.02x = -72 \] This means SP2 is greater than SP1, which means my initial assignment of SP1 and SP2 might be swapped for the difference calculation.
Let's recheck the discounts:
A single discount of 30% means 70% of MP. (SP1 = 0.70x).
Successive discounts of 20% and 10% mean 72% of MP. (SP2 = 0.72x).
The difference is $0.72x - 0.70x = 0.02x$.
\[ 0.02x = 72 \]
\[ x = \frac{72}{0.02} = \frac{72}{\frac{2}{100}} = \frac{72 \times 100}{2} = 36 \times 100 \]
\[ x = 3,600 \]
The marked price is Rs. 3,600.

Step 4: Final Answer:
The marked price is Rs. 3,600.

Answer 2

Rather than setting up an equation, this approach checks each candidate marked price directly against both discount schemes to see which one produces a difference of exactly Rs. 72.

1. 3,600: With a single 30% discount, the selling price is \( 3600 \times 0.70 = 2520 \). With successive discounts of 20% and 10%, the price after the first discount is \( 3600 \times 0.80 = 2880 \), and after the second discount \( 2880 \times 0.90 = 2592 \). The difference is \( 2592 - 2520 = 72 \), which matches the given condition exactly.
2. 3,000: Single 30% discount gives \( 3000 \times 0.70 = 2100 \). Successive discounts give \( 3000 \times 0.80 \times 0.90 = 2160 \). The difference is \( 2160 - 2100 = 60 \), not 72, so this is not the marked price.
3. 2,500: Single discount gives \( 2500 \times 0.70 = 1750 \). Successive discounts give \( 2500 \times 0.72 = 1800 \). The difference is \( 1800 - 1750 = 50 \), which does not match.
4. 2,400: Single discount gives \( 2400 \times 0.70 = 1680 \). Successive discounts give \( 2400 \times 0.72 = 1728 \). The difference is \( 1728 - 1680 = 48 \), which also does not match.

Only a marked price of Rs. 3,600 produces the required difference of Rs. 72 between the two discount schemes.

Therefore, the correct answer is 3,600.