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In the given question two quantities are...

In the given question two quantities are given one as quantity -I and the other is quantity II you have to determine relationship between these two quantities and choose the appropriate options as given
Quantity-I:The price of a bike is `₹28,000` mr A gives a discount of 12% on the whole while B gives a discount of 12% on first `₹20,000` and 8% on rest `₹8000` what is difference between their selling price on the transaction
Quantity II:A trader has 600 kg of rice he sells a part o fit at 15% profit and remaining quantity at 20% loss and suffers a loss of 6% on whole quantity, what is quantity of rice he sold at 20% loss

A

`quantity-IgtII`

B

`quantity IltII`

C

`quantity IleII`

D

`quantity IgeII`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will break it down into two parts: Quantity I and Quantity II. ### Quantity I: Selling Price of the Bike 1. **Calculate the Selling Price of Mr. A:** - The price of the bike = ₹28,000 - Discount given by Mr. A = 12% - Selling Price (SP) of A = Price - Discount - Discount = 12% of ₹28,000 = (12/100) * 28,000 = ₹3,360 - SP of A = ₹28,000 - ₹3,360 = ₹24,640 2. **Calculate the Selling Price of Mr. B:** - Mr. B gives a discount of 12% on the first ₹20,000 and 8% on the remaining ₹8,000. - Discount on the first ₹20,000 = 12% of ₹20,000 = (12/100) * 20,000 = ₹2,400 - Selling Price for the first ₹20,000 = ₹20,000 - ₹2,400 = ₹17,600 - Discount on the remaining ₹8,000 = 8% of ₹8,000 = (8/100) * 8,000 = ₹640 - Selling Price for the remaining ₹8,000 = ₹8,000 - ₹640 = ₹7,360 - Total Selling Price of B = ₹17,600 + ₹7,360 = ₹24,960 3. **Calculate the Difference in Selling Prices:** - Difference = SP of A - SP of B = ₹24,640 - ₹24,960 = -₹320 - Since we are looking for the absolute difference, we take | -320 | = ₹320. ### Quantity II: Quantity of Rice Sold at 20% Loss 1. **Let the total quantity of rice = 600 kg.** 2. **Let X kg be the quantity sold at 15% profit.** - Selling Price for X kg at 15% profit = X * (1 + 0.15) = 1.15X 3. **The remaining quantity sold at 20% loss:** - Remaining quantity = 600 - X kg - Selling Price for (600 - X) kg at 20% loss = (600 - X) * (1 - 0.20) = (600 - X) * 0.80 = 480 - 0.80X 4. **Total Cost Price of 600 kg of rice:** - Assume cost price of 1 kg = ₹1, then total cost price = ₹600. 5. **Total Selling Price (SP) with a loss of 6%:** - Loss of 6% on ₹600 = 600 * (1 - 0.06) = ₹564. 6. **Setting up the equation:** - Total SP = SP from X kg + SP from (600 - X) kg - 564 = 1.15X + (480 - 0.80X) - 564 = 1.15X + 480 - 0.80X - Combine like terms: 564 = 0.35X + 480 - 564 - 480 = 0.35X - 84 = 0.35X - X = 84 / 0.35 = 240 kg 7. **Quantity sold at 20% loss:** - Quantity sold at 20% loss = 600 - X = 600 - 240 = 360 kg. ### Final Comparison - Quantity I = ₹320 - Quantity II = 360 kg Since ₹320 is less than 360 kg, we conclude: **Answer:** Quantity I < Quantity II
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