An article when sold at a gain of 5%, yields Rs. 15 more than when sold at a loss of 5%. The cost price will be
Rs. 150
Finding the Cost Price of an Article with Gain and Loss Difference
This problem involves calculating the original cost price (CP) of an article when the difference between its selling price at a certain percentage gain and its selling price at the same percentage loss is given. We are told that selling the article at a gain of 5% yields Rs. 15 more than when it is sold at a loss of 5%.
Setting up the Problem
Let the Cost Price of the article be Rs. \(x\).
We need to find the selling price in two different scenarios:
- When there is a gain of 5%.
- When there is a loss of 5%.
Calculating Selling Price with Gain
When the article is sold at a gain of 5%, the gain amount is 5% of the cost price. Gain = \(5\%\) of \(x = \frac{5}{100} \times x = 0.05x\)
The Selling Price (SP1) in this case will be the Cost Price plus the Gain: SP1 = \(x + 0.05x = 1.05x\)
Calculating Selling Price with Loss
When the article is sold at a loss of 5%, the loss amount is 5% of the cost price. Loss = \(5\%\) of \(x = \frac{5}{100} \times x = 0.05x\)
The Selling Price (SP2) in this case will be the Cost Price minus the Loss: SP2 = \(x - 0.05x = 0.95x\)
Using the Given Difference in Selling Prices
According to the problem, the selling price at a gain of 5% is Rs. 15 more than the selling price at a loss of 5%. So, SP1 - SP2 = 15
Substitute the expressions for SP1 and SP2 into this equation: \(1.05x - 0.95x = 15\)
Solving for the Cost Price (x)
Simplify the equation:
\((1.05 - 0.95)x = 15\)
\(0.10x = 15\)
To find \(x\), divide 15 by 0.10:
\(x = \frac{15}{0.10}\)
\(x = \frac{15}{\frac{10}{100}}\)
\(x = 15 \times \frac{100}{10}\)
\(x = 15 \times 10\)
\(x = 150\)
Conclusion
The Cost Price of the article is Rs. 150.
This matches the first option provided.
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?
