The S.P. of a washing machine is \(1\frac{1}{4}\) of its C.P. Find the gain percent.
25%
Calculating Gain Percent: Washing Machine Example
The question asks us to find the gain percent when the Selling Price (S.P.) of a washing machine is \(1\frac{1}{4}\) times its Cost Price (C.P.). Understanding the relationship between S.P., C.P., Gain, and Gain Percent is key here.
Understanding the Relationship between S.P. and C.P.
We are given that the S.P. is \(1\frac{1}{4}\) of the C.P.
First, let's convert the mixed fraction \(1\frac{1}{4}\) into an improper fraction:
\(1\frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{5}{4}\)
So, the given relationship is:
S.P. = \(\frac{5}{4} \times \) C.P.
Calculating the Gain
Gain is the difference between the Selling Price and the Cost Price. If S.P. > C.P., there is a gain. In this case, since S.P. is \(\frac{5}{4}\) of C.P. (and \(\frac{5}{4} > 1\)), the S.P. is greater than the C.P., which means there is a gain.
Gain = S.P. - C.P.
Substitute the given relationship:
Gain = \(\frac{5}{4} \times \) C.P. - C.P.
To subtract C.P., we can write C.P. as \(\frac{4}{4} \times \) C.P.
Gain = \(\frac{5}{4} \times \) C.P. - \(\frac{4}{4} \times \) C.P.
Gain = \(\left(\frac{5}{4} - \frac{4}{4}\right) \times \) C.P.
Gain = \(\frac{1}{4} \times \) C.P.
The gain is \(\frac{1}{4}\) of the Cost Price.
Calculating the Gain Percent
The formula for Gain Percent is:
Gain Percent = \(\frac{\text{Gain}}{\text{C.P.}} \times 100\%\)
Substitute the value of Gain we found (\(\frac{1}{4} \times \) C.P.) into the formula:
Gain Percent = \(\frac{\frac{1}{4} \times \text{C.P.}}{\text{C.P.}} \times 100\%\)
The C.P. in the numerator and the denominator cancels out:
Gain Percent = \(\frac{1}{4} \times 100\%\)
Gain Percent = \(\frac{100}{4}\%\)
Gain Percent = \(25\%\)
Thus, the gain percent is 25%.
Summary of Calculations
| Description | Calculation | Result |
|---|---|---|
| Given Relationship | S.P. = \(1\frac{1}{4} \times\) C.P. | S.P. = \(\frac{5}{4} \times\) C.P. |
| Calculate Gain | Gain = S.P. - C.P. | Gain = \(\frac{1}{4} \times\) C.P. |
| Calculate Gain Percent | \(\frac{\text{Gain}}{\text{C.P.}} \times 100\%\) | \(\frac{\frac{1}{4} \text{C.P.}}{\text{C.P.}} \times 100\% = 25\%\) |
Revision Table: Profit and Loss Basics
| Term | Definition | Formula |
|---|---|---|
| Cost Price (C.P.) | The price at which an article is purchased. | - |
| Selling Price (S.P.) | The price at which an article is sold. | - |
| Gain or Profit | When S.P. > C.P. | Gain = S.P. - C.P. |
| Loss | When C.P. > S.P. | Loss = C.P. - S.P. |
| Gain Percent | Gain expressed as a percentage of C.P. | Gain% = \(\frac{\text{Gain}}{\text{C.P.}} \times 100\) |
| Loss Percent | Loss expressed as a percentage of C.P. | Loss% = \(\frac{\text{Loss}}{\text{C.P.}} \times 100\) |
Additional Information: Working with Fractions and Percentages
- A percentage is a way of expressing a number as a fraction of 100. For example, 25% means \(\frac{25}{100} = \frac{1}{4}\).
- To convert a fraction to a percentage, multiply the fraction by 100. For example, \(\frac{1}{4} \times 100\% = 25\%\).
- To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.
- In profit and loss calculations, percentage gain or loss is always calculated with respect to the Cost Price unless otherwise stated.
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Important Questions from Successive Selling
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- The selling price of 24 articles is equal to the cost price of 26 articles. If, due to a change in market conditions, the selling price of each article decreases by $10\%$ and the cost price of each article increases by $5\%$, what will be the new gain or loss percentage (correct to two decimal places)?
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