The ratio of the cost price and selling price of an article is 10 ∶ 11. The gain per cent is:
10%
Calculating Gain Percentage from Cost Price Ratio
The problem asks us to find the gain percentage when the ratio of the cost price (CP) and the selling price (SP) of an article is given as 10 ∶ 11.
Let's define the terms:
- Cost Price (CP): The price at which an article is bought.
- Selling Price (SP): The price at which an article is sold.
- Gain: When SP is greater than CP. Gain = SP - CP.
- Gain Percentage: The gain expressed as a percentage of the cost price.
Given the ratio of CP to SP is 10 ∶ 11, we can represent the cost price and selling price using a variable. Let the common ratio be $x$.
So,
- Cost Price (CP) $= 10x$
- Selling Price (SP) $= 11x$
Since the selling price ($11x$) is greater than the cost price ($10x$), there is a gain. Let's calculate the gain amount.
Gain $= \text{SP} - \text{CP}$
Gain $= 11x - 10x$
Gain $= x$
Now, we need to calculate the gain percentage. The formula for gain percentage is:
$\text{Gain \%} = \frac{\text{Gain}}{\text{CP}} \times 100$
Substitute the values of Gain and CP into the formula:
$\text{Gain \%} = \frac{x}{10x} \times 100$
We can cancel out $x$ from the numerator and the denominator (assuming $x \neq 0$, which it must be for a price).
$\text{Gain \%} = \frac{1}{10} \times 100$
$\text{Gain \%} = 10$
So, the gain percentage is 10%.
Let's verify with an example. If CP = ₹10 and SP = ₹11 (ratio 10:11), the gain is ₹$11 - 10 = ₹1$. The gain percentage is $\frac{1}{10} \times 100 = 10\%$. This matches our calculation.
This calculation shows that when the ratio of cost price to selling price is 10:11, the gain is indeed 10%.
| Parameter | Value |
|---|---|
| Ratio CP : SP | 10 : 11 |
| Assume CP | 10x |
| Assume SP | 11x |
| Gain (SP - CP) | 11x - 10x = x |
| Gain % Formula | $\frac{\text{Gain}}{\text{CP}} \times 100$ |
| Gain % Calculation | $\frac{x}{10x} \times 100 = 10\%$ |
Revision Table: Key Concepts in Profit and Loss
| Concept | Formula | Condition |
|---|---|---|
| Gain (Profit) | SP - CP | SP > CP |
| Loss | CP - SP | CP > SP |
| Gain Percentage | $\frac{\text{Gain}}{\text{CP}} \times 100$ | SP > CP |
| Loss Percentage | $\frac{\text{Loss}}{\text{CP}} \times 100$ | CP > SP |
Additional Information: Understanding Ratios in Commerce Problems
Ratios are often used in commerce and business problems to represent relationships between different quantities like cost price, selling price, marked price, discount, etc. When a ratio is given, like CP : SP = $a : b$, it means that for some value $x$, CP $= ax$ and SP $= bx$. This method simplifies calculations, especially when dealing with percentages, as the variable $x$ often cancels out, as seen in the gain percentage calculation above.
Using ratios helps in quickly determining if there is a gain or loss. If the ratio of SP to CP ($b/a$) is greater than 1, there is a gain. If it is less than 1, there is a loss. In our case, the ratio SP : CP is 11 : 10, or $11/10 = 1.1$, which is greater than 1, indicating a gain.
The gain or loss percentage is always calculated with respect to the cost price, unless otherwise specified.
Similar Questions
Chamanlal, Arshad and Jagit Singh contested an election. All the votes polled were valid. Arshad got 35% of the total votes. For every 35 votes Chamanlal got 14 votes. The winner got 4950 more votes than the person who received the least number of votes. Find the total number of votes polled.
A father gives 8% of his monthly income to both his sons as pocket money. The elder son gets 85% of the total amount given to both sons. He spends 90% of the amount and saves Rs. 17. What is the monthly income of his father?
In an examination a candidate had to sit for three papers A, B, and C. The candidate secured 75% marks in Paper A, 80% marks in Paper B, and 60% marks in Paper C. If the weightage assigned to Papers A, B, and C were 40%, 50% and 10%, respectively, then find the weighted percentage of marks obtained by the candidate, when all the three papers were taken together.
The sum of two numbers is 680. If the bigger number is decreased by 15% and the smaller number is increased by 15%, then the resultant numbers are equal. Find the smaller number.
A number is decreased by 20% to get another number. The number so obtained is increased by 200% to get a third number. The difference of the third number and the original number is what percentage more or less than the difference of second and the third number?
In the first year the population of a town decreased by 5% due to the Corona virus first wave. In the next year it decreased again by 5% due to the second wave and in the third year it increased by 5%. At the end of the third year the population was 9,47,625. What was the population at the beginning of the first year?
In an election between two candidates, a candidate who gets 64% of the votes polled is elected by a majority of 252 votes. What is the total number of votes polled?
Out of an earning of Rs. 720, Pankaj spends 65%. How much does he save?
The number of units manufactured by a company A was 12500 units in 2019 and 10625 units in 2020. While in company B, the production fell from 34000 units in 2019 to 30600 units in 2020. If X and Y are the percentage decrease in the number of units manufactured by company A and B respectively from 2019 to 2020, then what will be the ratio of X and Y?
In a constituency, 85% of the total number of people on the electoral roll cast their votes during an election. 10% of the votes cast were declared invalid. If there were 3,00,000 people on the electoral roll, and Dharam secured 1,37,700 valid votes, what percentage of the total number of valid votes did Dharam secure?
Important Questions from Percentage
In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination?
What is the value of 9% of 5500 + 2.4% of 1100 - 40% of 1600?
Population of a village is 7960 in which 4660 are female. If in that village 60% are literate in which 70% female are literate, then what is the number of literate male ?
The numbers of students of three classes of a school are in the ratio 4 : 5 : 6. If numbers of students in these classes increase by 25%, 20% and 25% respectively, then ratio of numbers of students will become:
In an examination, Ram obtained 20 % more than Ashok but 10% less than Rajesh. If the marks obtained by Ashok is 1080. Then the Percentage marks obtained by Rajesh if the full marks is 2000 ;
