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.
Important Questions from Discount and MP
A single discount equivalent to two successive discounts of 15% and 25% is:
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A shopkeeper marks the marked price of an article 30% more than its real price and offers 10% discount. What is the gain percentage?
An article was sold for Rs. 1,215 after giving a discount of 19%. If a discount of 17.5% is given, then for how much (in Rs.) should the article be sold?
