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
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
