In a school of 750 boys, 34% are Muslims, 42% Hindus, 12% Sikhs and the rest belong to other communities. How many boys are from other community?
90
Solving the School Community Question
The question asks us to find the number of boys belonging to communities other than Muslims, Hindus, and Sikhs in a school of 750 boys.
Understanding the Given Information
We are given the total number of boys in the school and the percentages of boys belonging to three specific communities:
- Total number of boys = 750
- Percentage of Muslim boys = 34%
- Percentage of Hindu boys = 42%
- Percentage of Sikh boys = 12%
The remaining percentage belongs to other communities.
Calculating the Percentage of Boys from Other Communities
The total percentage of all communities must add up to 100%. We can find the percentage of boys from other communities by subtracting the percentages of Muslims, Hindus, and Sikhs from 100%.
Percentage of boys from other communities $= 100\% - (\text{Percentage of Muslims} + \text{Percentage of Hindus} + \text{Percentage of Sikhs})$
Percentage of boys from other communities $= 100\% - (34\% + 42\% + 12\%)$
First, let's sum the percentages of the known communities:
\(34\% + 42\% + 12\% = (34 + 42 + 12)\%\)
\(34 + 42 = 76\)
\(76 + 12 = 88\)
So, the total percentage of Muslim, Hindu, and Sikh boys is 88%.
Now, subtract this from 100% to find the percentage of boys from other communities:
Percentage of boys from other communities $= 100\% - 88\% = 12\%$
Calculating the Number of Boys from Other Communities
We know that 12% of the total boys belong to other communities. To find the number of boys, we calculate 12% of 750.
Number of boys from other communities $= 12\% \text{ of } 750$
To calculate a percentage of a number, we convert the percentage to a decimal or fraction and multiply by the number.
\(12\% = \frac{12}{100}\)
Number of boys from other communities $= \frac{12}{100} \times 750$
We can simplify this calculation:
\(\frac{12}{100} \times 750 = \frac{12 \times 750}{100}\)
We can cancel out a 10 from 750 and 100:
\(\frac{12 \times 75}{10}\)
We can simplify by dividing both 12 and 10 by 2:
\(\frac{6 \times 75}{5}\)
Now, divide 75 by 5:
\(\frac{6 \times 15}{1}\)
\(6 \times 15 = 90\)
So, the number of boys from other communities is 90.
Summary of Percentages and Numbers
| Community | Percentage of Boys | Number of Boys (Calculation) | Number of Boys |
|---|---|---|---|
| Muslims | 34% | \(\frac{34}{100} \times 750\) | 255 |
| Hindus | 42% | \(\frac{42}{100} \times 750\) | 315 |
| Sikhs | 12% | \(\frac{12}{100} \times 750\) | 90 |
| Other Communities | 12% | \(\frac{12}{100} \times 750\) | 90 |
| Total | 100% | \(255 + 315 + 90 + 90 = 750\) |
The calculation confirms that 90 boys are from other communities.
Conclusion
By calculating the percentage of boys not belonging to the specified communities and then finding that percentage of the total number of boys, we determined that 90 boys are from other communities.
Revision Table: School Boys Community Distribution
| Concept | Explanation | Formula/Method |
|---|---|---|
| Total Percentage | The sum of percentages of all categories must be 100%. | Sum of percentages = 100% |
| Percentage of Remaining Category | Calculated by subtracting known percentages from 100%. | Percentage of Other $= 100\%$ - (Sum of known percentages) |
| Number from Percentage | To find the number represented by a percentage of a total. | Number = \(\frac{\text{Percentage}}{100} \times \text{Total}\) |
Additional Information: Working with Percentages
Percentages are a way of expressing a part of a whole in terms of 100. The word "percent" means "per hundred".
- To convert a percentage to a decimal, divide by 100. For example, \(12\% = \frac{12}{100} = 0.12\).
- To convert a percentage to a fraction, write it as a fraction with a denominator of 100 and simplify if possible. For example, \(12\% = \frac{12}{100} = \frac{3}{25}\).
- When calculating a percentage "of" a number, "of" means multiplication. For example, 12% of 750 means \(0.12 \times 750\) or \(\frac{12}{100} \times 750\).
Understanding percentages is crucial for solving many problems involving proportions, discounts, increases, and decreases, as seen in this school community distribution example.
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