Question

A shopkeeper marks an item 40 % above its cost price. He offers two successive discounts of 10 % and 20 % on the marked price. If the selling price is 504 rupees, what is the cost price of the item?

• A. 400 rupees
• B. 450 rupees
• C. 500 rupees
• D. 554 rupees

Hint:

For successive discounts, calculate the final selling price by applying each discount sequentially: \( \text{SP} = \text{MP} \times (1 - \frac{d_1}{100}) \times (1 - \frac{d_2}{100}) \), then solve for CP.

Answer 1

The Correct Option is C

The objective is to determine the cost price of an item, given its marked price, sequential discounts, and the final selling price.

1. Key Definitions:

- Cost Price (CP): The initial purchase price of the item.
- Marked Price (MP): The price after a 40% increase over the CP.
- Successive Discounts: Multiple discounts applied sequentially to the marked price.
- Selling Price (SP): The final price after all discounts are applied.

2. Provided Data:

- Marked Price = CP + 40% of CP = \( 1.4 \times \text{CP} \)
- Discounts = 10% and 20% applied consecutively
- Selling Price = Rs 504

3. Derivation of Selling Price in terms of CP:

After the first discount of 10%: \[ \text{Price after first discount} = 1.4 \times \text{CP} \times (1 - 0.10) = 1.4 \times \text{CP} \times 0.9 = 1.26 \times \text{CP} \] After the second discount of 20%: \[ \text{SP} = 1.26 \times \text{CP} \times (1 - 0.20) = 1.26 \times \text{CP} \times 0.8 = 1.008 \times \text{CP} \] Since SP = 504: \[ 1.008 \times \text{CP} = 504 \Rightarrow \text{CP} = \frac{504}{1.008} = 500 \]

Final Determination:

The cost price of the item is calculated to be Rs 500.