The percentage profit earned by selling an article for ₹1,910 is equal to the percentage loss incurred by selling the same article for ₹1,690. At what price (in) should the article be sold to make a 12% profit?
Understanding the Profit and Loss Scenario
The question describes a situation where selling an article results in a specific percentage profit, and selling the same article at a different price results in the same percentage loss. We need to find the cost price first, and then determine the selling price needed to achieve a 12% profit.
Let's denote:
- Cost Price (CP) as $C$
- Selling Price 1 (SP1) = ₹1,910 (where there is a profit)
- Selling Price 2 (SP2) = ₹1,690 (where there is a loss)
The problem states that the percentage profit earned at SP1 is equal to the percentage loss incurred at SP2.
Calculating the Cost Price (CP)
The profit when selling at ₹1,910 is $SP1 - C = 1910 - C$.
The loss when selling at ₹1,690 is $C - SP2 = C - 1690$.
The percentage profit is calculated as: $$ \text{Percentage Profit} = \frac{\text{Profit}}{C} \times 100 = \frac{1910 - C}{C} \times 100 $$
The percentage loss is calculated as: $$ \text{Percentage Loss} = \frac{\text{Loss}}{C} \times 100 = \frac{C - 1690}{C} \times 100 $$
According to the question, these percentages are equal:
$$ \frac{1910 - C}{C} \times 100 = \frac{C - 1690}{C} \times 100 $$We can cancel out the '× 100' and divide by $C$ (since $C$ cannot be zero) from both sides:
$$ 1910 - C = C - 1690 $$Now, let's solve for $C$. Rearrange the terms:
$$ 1910 + 1690 = C + C $$ $$ 3600 = 2C $$ $$ C = \frac{3600}{2} $$ $$ C = 1800 $$So, the Cost Price (CP) of the article is ₹1,800.
Calculating the Selling Price for 12% Profit
The goal is to find the selling price (let's call it $SP_{new}$) that yields a 12% profit.
The Cost Price is $C = ₹1,800$.
The desired profit percentage is 12%.
First, calculate the profit amount:
$$ \text{Profit Amount} = 12\% \text{ of } C $$ $$ \text{Profit Amount} = \frac{12}{100} \times 1800 $$ $$ \text{Profit Amount} = 12 \times 18 $$ $$ \text{Profit Amount} = 216 $$The profit amount needed is ₹216.
Now, calculate the new selling price by adding the profit amount to the cost price:
$$ SP_{new} = C + \text{Profit Amount} $$ $$ SP_{new} = 1800 + 216 $$ $$ SP_{new} = 2016 $$Therefore, the article should be sold for ₹2,016 to make a 12% profit.
Conclusion
The calculated selling price to achieve a 12% profit is ₹2,016. This matches option 1.
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Important Questions from Profit and Loss
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