Solving the Reduced Apple Price Problem
This problem involves calculating the reduced price of apples per dozen after a percentage decrease in price allows for purchasing more quantity for the same total cost. We need to find the final price per dozen based on the given information.
Calculating Original and Reduced Price Per Apple
Let the original price of an apple be '$P$' rupees.
The price reduction is 20%, so the new reduced price per apple is $P \times (1 - 0.20) = 0.8P$ rupees.
Let the original quantity of apples bought for ₹54 be '$N$' apples.
The original total cost equation is:
$ N \times P = 54 \quad \cdots (1) $After the price reduction, the man can buy 10 apples more for the same ₹54. The new quantity is '$N + 10$' apples.
The new total cost equation is:
$ (N + 10) \times 0.8P = 54 \quad \cdots (2) $Expand equation (2):
$ 0.8NP + 8P = 54 $Substitute the value of '$NP$' from equation (1) into the expanded equation (2):
$ 0.8(54) + 8P = 54 $Calculate $0.8 \times 54$:
$ 43.2 + 8P = 54 $Now, solve for the original price per apple '$P$':
$ 8P = 54 - 43.2 $ $ 8P = 10.8 $ $ P = \frac{10.8}{8} $ $ P = 1.35 $So, the original price per apple was ₹1.35.
The reduced price per apple is $0.8P$:
$ \text{Reduced Price per Apple} = 0.8 \times 1.35 $ $ \text{Reduced Price per Apple} = 1.08 $The reduced price per apple is ₹1.08.
Determining Reduced Price Per Dozen
A dozen contains 12 items.
To find the reduced price per dozen apples, multiply the reduced price per apple by 12:
$ \text{Reduced Price per Dozen} = \text{Reduced Price per Apple} \times 12 $ $ \text{Reduced Price per Dozen} = 1.08 \times 12 $ $ \text{Reduced Price per Dozen} = 12.96 $The reduced price of apples per dozen is ₹12.96.
Important Questions from Profit and Loss
Ram bought a chair at 35% discount on its market price, Had Ram got no discount, he would have had to pay ₹245 more. How much did Ram pay for the chair?
A shopkeeper bought an item for Rs. 4,500 and sold it at a loss of 5%. From this money, he bought another item and sold it at a profit of 10%. What is his overall profit?
A man sells two articles at Rs. 9,180 each. He gains 8% on one article and loses 15% on the other. His overall profit or loss is:
A shopkeeper selling an article for ₹46 loses 8%. In order to gain 6%, what should be the selling price of the article?
Rahul purchased 80 items from the market. 25% items of the total items were defective and the remaining items were sold at 50% profit. What will be the overall profit percentage?
