Instead of marking up an article by 20%, by mistake, a shopkeeper marked it down by 20%. Furthermore, a discount of 6.25% was offered on the marked price of all articles in the shop. In this transaction, the shopkeeper incurred a loss of Rs. 3,750. What was the actual selling price (in Rs.) that the article was supposed to be sold at?
Answer (2)
To solve this problem, we need to determine the actual selling price that the article was supposed to be sold at if it had been marked up by 20% instead of being marked down. Let's break this down step by step.
Understanding the Problem:
The original price of the article is denoted as P .
Instead of marking up the price by 20%, the shopkeeper mistakenly marked it down by 20%.
Then, a further discount of 6.25% was offered on this incorrectly marked price.
This led to a loss of Rs. 3,750.
Calculating the Incorrect Marked Price:
The shopkeeper marked down the article by 20%, meaning the incorrect marked price is 0.8 P .
Calculating the Discounted Selling Price:
A further 6.25% discount was applied to the incorrectly marked price. This means the selling price was 0.9375 × 0.8 P = 0.75 P (since 0.8 × 0.9375 = 0.75 ).
Determining the Loss:
The loss incurred was Rs. 3,750.
Originally, if marked up by 20%, the selling price should have been 1.2 P .
Thus, we know that 1.2 P − 0.75 P = 3 , 750 .
Solving for the Original Price P : 1.2 P − 0.75 P = 3 , 750 0.45 P = 3 , 750 P = 0.45 3 , 750 P = 8 , 333.33
Finding the Correct Selling Price:
The correct selling price with a 20% markup should have been 1.2 × 8 , 333.33 .
1.2 × 8 , 333.33 = 10 , 000
Therefore, the article was supposed to be sold at Rs. 10,000. This calculation ensures that all details relating to the percentage markup, markdown, discount, and the resulting loss are accounted for precisely.
The article was originally priced at Rs. 8,333.33, and after a 20% markup, it should have been sold at Rs. 10,000. Instead, due to a mistake of marking it down by 20% and applying a discount, the shopkeeper incurred a loss of Rs. 3,750. The intended selling price was Rs. 10,000.
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