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?
Rs. 50,000
Solving Profit and Loss Problems: Finding Initial Value
This problem involves calculating the initial value of a car based on two consecutive sale transactions involving profit and loss percentages.
Understanding the Transactions
Let's break down the information given:
- A man sells a car to his friend at a loss of 10%.
- The friend sells the car for Rs. 54000, making a profit of 20%.
We need to find the initial value of the car, which is the cost price for the first man.
Step-by-Step Calculation
Let the initial value (Cost Price for the first man) be \(CP_1\).
The first man sells the car at a 10% loss. The Selling Price for the first man (\(SP_1\)) is given by:
\(SP_1 = CP_1 - (10\% \text{ of } CP_1)\)
\(SP_1 = CP_1 - 0.10 \times CP_1\)
\(SP_1 = CP_1 (1 - 0.10)\)
\(SP_1 = 0.90 \times CP_1\)
This \(SP_1\) is the Cost Price for the friend (\(CP_2\)).
\(CP_2 = SP_1 = 0.90 \times CP_1\)
The friend sells the car for Rs. 54000, making a profit of 20%. The Selling Price for the friend (\(SP_2\)) is given by:
\(SP_2 = CP_2 + (20\% \text{ of } CP_2)\)
\(SP_2 = CP_2 + 0.20 \times CP_2\)
\(SP_2 = CP_2 (1 + 0.20)\)
\(SP_2 = 1.20 \times CP_2\)
We are given that \(SP_2 = \text{Rs. } 54000\). So, we have:
\(1.20 \times CP_2 = 54000\)
Now, substitute the expression for \(CP_2\) from the first transaction into this equation:
\(1.20 \times (0.90 \times CP_1) = 54000\)
Multiply the decimal values:
\(1.20 \times 0.90 = 1.08\)
So, the equation becomes:
\(1.08 \times CP_1 = 54000\)
To find \(CP_1\), divide 54000 by 1.08:
\(CP_1 = \frac{54000}{1.08}\)
\(CP_1 = \frac{5400000}{108}\)
Performing the division:
| Calculation | Result |
|---|---|
| \(5400000 \div 108\) | \(50000\) |
So, the initial value of the car (\(CP_1\)) was Rs. 50000.
Verification
Let's check if this initial value works with the given conditions:
- Initial value \(CP_1 = \text{Rs. } 50000\).
- Man sells at 10% loss: \(SP_1 = 50000 - 0.10 \times 50000 = 50000 - 5000 = \text{Rs. } 45000\).
- Friend buys at \(CP_2 = \text{Rs. } 45000\).
- Friend sells for Rs. 54000, making a profit. Profit = \(54000 - 45000 = \text{Rs. } 9000\).
- Profit percentage = \(\frac{\text{Profit}}{CP_2} \times 100 = \frac{9000}{45000} \times 100 = \frac{9}{45} \times 100 = \frac{1}{5} \times 100 = 20\%\).
The calculated profit percentage matches the 20% profit mentioned in the problem, confirming our initial value is correct.
The initial value of the car was Rs. 50000.
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?
By selling a horse for Rs. 670, a tradesman would lose 5%. At what price must he sell it to gain 5%?
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?
