A shopkeeper marked up a shirt 50% above the cost price and allows successive discounts of 111/9% and 10% on it. If the difference between profit earned and discount given is Rs. 200 then find the marked price of the shirt?
Question
A shopkeeper marked up a shirt 50% above the cost price and allows successive discounts of 111/9% and 10% on it. If the difference between profit earned and discount given is Rs. 200 then find the marked price of the shirt?
Solution
Step 1: Let's assume the cost price of the shirt is Rs. x.
Step 2: The shopkeeper marked up the price by 50%, so the marked price becomes Rs. 1.5x.
Step 3: The first discount is 111/9% which is equivalent to 12.33%. So, the price after the first discount is 1.5x * (1 - 12.33/100) = 1.5x * 0.8767 = Rs. 1.315x.
Step 4: The second discount is 10%. So, the price after the second discount is 1.315x * (1 - 10/100) = 1.315x * 0.9 = Rs. 1.1835x.
Step 5: The profit earned is the selling price (after discounts) minus the cost price, which is 1.1835x - x = 0.1835x.
Step 6: The total discount given is the marked price minus the selling price, which is 1.5x - 1.1835x = 0.3165x.
Step 7: According to the problem, the difference between the profit earned and the discount given is Rs. 200. So, we have 0.3165x - 0.1835x = 200, which simplifies to 0.133x = 200.
Step 8: Solving for x, we get x = 200 / 0.133 = Rs. 1503.76 (approximately).
Step 9: The marked price of the shirt is 1.5x = 1.5 * 1503.76 = Rs. 2255.64 (approximately).
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