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
Rohit buys 8 pens and 4 pencils for Rs. 2400. He sells pencils at a profit of 20 percent and pens at the loss of 10 percent. If his overall profit is Rs. 240, then what is the sum of the cost price of one pen and one pencil?
A man sells a car to his friend at the loss of 10 %; who in return sells it for Rs. 54000 making a profit of 20 %. What was the initial value of the car?
An article was sold at a loss of 24%. If it were sold for Rs. 1,596 more, then there would have been a gain of 18%, The cost price of the article is:
The cost price of an article is Rs.6,450. If it sold at a profit 16%, how much would be its selling price?
If the selling price of 7 articles is equal to the cost price of 6 articles, then what is the percentage loss?
