The cost price of a toy is ₹210. What should be its marked price so that, after a discount of 5%, the shopkeeper gains 90%?
₹420
Calculate Marked Price with Discount and Gain
This question asks us to find the marked price (MP) of a toy. We are given the cost price (CP), the discount percentage, and the desired profit percentage (gain). The goal is to determine the price label (MP) such that after applying the discount, the shopkeeper makes the specified profit.
Step 1: Calculate the Selling Price (SP) needed for Profit
First, we determine the selling price required to achieve the target profit.
- The Cost Price (CP) is ₹210.
- The desired profit gain is 90%.
The Selling Price (SP) is calculated using the formula:
\( SP = CP \times (1 + \frac{Gain\%}{100}) \)
Substituting the values:
\( SP = 210 \times (1 + \frac{90}{100}) = 210 \times (1 + 0.9) = 210 \times 1.9 = 399 \)
So, the required Selling Price is ₹399.
Step 2: Calculate the Marked Price (MP) using the Discount
Now, we use the calculated Selling Price and the discount information to find the Marked Price.
- The Selling Price (SP) required is ₹399.
- The discount offered is 5%.
The relationship between Selling Price (SP), Marked Price (MP), and Discount Percentage is:
\( SP = MP \times (1 - \frac{Discount\%}{100}) \)
To find the Marked Price (MP), we rearrange the formula:
\( MP = \frac{SP}{(1 - \frac{Discount\%}{100})} \)
Substitute the known values:
\( MP = \frac{399}{(1 - \frac{5}{100})} = \frac{399}{(1 - 0.05)} = \frac{399}{0.95} \)
Calculating the final value:
\( MP = 420 \)
Therefore, the Marked Price should be ₹420.
Final Answer Summary
The calculation confirms that setting the marked price at ₹420 allows the shopkeeper to offer a 5% discount and still achieve a 90% gain on the initial cost price of ₹210.
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Important Questions from Discount and MP
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I. Two successive discounts of 15% and 20%.
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III. Buy 6 get 4 free - A shopkeeper is given a 10% trade discount and a 5% scheme discount (free units). On purchasing 100 units priced at ₹50 each, what is the trade discount amount?
- What is the equivalent single discount for successive discounts of 20% and 10%?
- Rahul buys a box of pens (listed price of ₹900) with a trade discount of 30%. What is the net price?
