Analyzing the Selling Price and Cost Price Relationship
The problem starts with a relationship between the selling price (SP) of 24 articles and the cost price (CP) of 26 articles. We are given:
Selling Price of 24 articles = Cost Price of 26 articles
Let $SP$ represent the selling price of one article and $CP$ represent the cost price of one article. We can write this relationship mathematically as:
$24 \times SP = 26 \times CP$To understand the base ratio between the SP and CP, we can rearrange this equation:
$\frac{SP}{CP} = \frac{26}{24}$Simplifying the fraction gives us:
$\frac{SP}{CP} = \frac{13}{12}$This ratio tells us that for every $12$ units of cost price, the selling price is $13$ units. We can express this using a common multiplier, say $k$. So, let $SP = 13k$ and $CP = 12k$.
From this initial setup, we can see there's a gain since $SP > CP$. The initial gain is $SP - CP = 13k - 12k = k$. The initial gain percentage is $\frac{\text{Gain}}{CP} \times 100 = \frac{k}{12k} \times 100 = \frac{100}{12} \approx 8.33\%$. However, the question asks for the new gain/loss percentage after specific changes.
Calculating New Selling and Cost Prices
The problem states that market conditions changed, affecting the prices:
- The selling price of each article decreases by $10\%$.
- The cost price of each article increases by $5\%$.
Let's calculate the new selling price ($SP_{new}$) and the new cost price ($CP_{new}$):
New Selling Price ($SP_{new}$):
The original SP was $13k$. A $10\%$ decrease means the new SP is $100\% - 10\% = 90\%$ of the original SP.
$SP_{new} = SP \times (1 - 10\%) = 13k \times (1 - 0.10) = 13k \times 0.90$ $SP_{new} = 11.7k$New Cost Price ($CP_{new}$):
The original CP was $12k$. A $5\%$ increase means the new CP is $100\% + 5\% = 105\%$ of the original CP.
$CP_{new} = CP \times (1 + 5\%) = 12k \times (1 + 0.05) = 12k \times 1.05$ $CP_{new} = 12.6k$Determining New Gain or Loss Percentage
Now, we compare the $SP_{new}$ and $CP_{new}$ to find the new profit or loss.
- $SP_{new} = 11.7k$
- $CP_{new} = 12.6k$
Since the new selling price ($11.7k$) is less than the new cost price ($12.6k$), there is a loss.
Calculate the New Loss Amount:
$ \text{Loss} = CP_{new} - SP_{new} $ $ \text{Loss} = 12.6k - 11.7k $ $ \text{Loss} = 0.9k $Calculate the New Loss Percentage:
The loss percentage is calculated based on the new cost price ($CP_{new}$).
$ \text{Loss Percentage} = \frac{\text{Loss}}{CP_{new}} \times 100 $ $ \text{Loss Percentage} = \frac{0.9k}{12.6k} \times 100 $The variable $k$ cancels out:
$ \text{Loss Percentage} = \frac{0.9}{12.6} \times 100 $ $ \text{Loss Percentage} = \frac{9}{126} \times 100 $Simplify the fraction $\frac{9}{126}$ by dividing both numerator and denominator by 9:
$ \text{Loss Percentage} = \frac{1}{14} \times 100 $ $ \text{Loss Percentage} = \frac{100}{14} $ $ \text{Loss Percentage} \approx 7.142857...\% $Rounding the loss percentage to two decimal places, we get $7.14\%$. Therefore, there is a loss of $7.14\%$.
Conclusion
After the changes in selling price (decrease by $10\%$) and cost price (increase by $5\%$), the overall result is a loss. The calculated new loss percentage is approximately $7.14\%$.
Comparing this result with the given options, the correct option is Loss $7.14\%$.
Important Questions from Successive Selling
By selling a watch at Rs. 840 a person loses 4%. Find the gain or loss if he sold it for Rs. 875?
Gaurav bought some articles at 5 for Rs. 6 and sold them at 10 for Rs. 11. His loss percentage is:
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
X sells goods to Y at a profit of 20 percent and Y sells the same goods to Z at a profit of 50 percent. If the cost price for Z is Rs 9000, then what is the cost of the goods for X?
Anil bought some articles at 6 for Rs. 8 and sold them at 10 for Rs. 12. His percentage loss or gain is:
