Grade Fraction of the population A 0.1 B 0.4 C 0.3 D 0.2
What is the least possible population of the class?
Determining Least Class Population from Grade Fractions
The problem asks for the minimum possible number of students in a class, given the fraction of students who received each grade (A, B, C, D).
The grade distribution is provided as:
| Grade | Fraction |
| A | 0.1 |
| B | 0.4 |
| C | 0.3 |
| D | 0.2 |
Analyzing Grade Fractions
The fractions represent the proportion of the total class population. To find the least possible population, we need to express these fractions in their simplest forms and find the Least Common Multiple (LCM) of their denominators.
- Grade A: $0.1 = \frac{1}{10}$
- Grade B: $0.4 = \frac{4}{10} = \frac{2}{5}$
- Grade C: $0.3 = \frac{3}{10}$
- Grade D: $0.2 = \frac{2}{10} = \frac{1}{5}$
Calculating the Least Common Multiple (LCM)
The denominators of the simplified fractions are 10 and 5.
The least common multiple (LCM) of 10 and 5 is the smallest positive integer that is divisible by both 10 and 5.
- Multiples of 10: 10, 20, 30, ...
- Multiples of 5: 5, 10, 15, 20, ...
The LCM(10, 5) is 10.
Finding the Least Possible Population
The least possible population of the class must be a number that allows for these exact fractional distributions. This number is the LCM of the denominators of the fractions.
Therefore, the least possible population of the class is 10.
This corresponds to Option D.
Important Questions from Percentage (Notes)
In an election between two candidates, a candidate who got $30\%$ of the total votes is defeated by $15000$ votes. The number of votes obtained by the winning candidate is:-
- Which of the following multipliers will increase a given number by 25.3 % ?
If A earns \(33\frac{1}{3}%\) more than B, then how much percent does B earn less than A?
- दो उम्मीदवारों के बीच एक कॉलेज चुनाव में, एक उम्मीदवार को कुल वैध मतों में से $55\%$ वोट मिले । $15\%$ वोट अवैध थे । यदि कुल वोट $15,200$ थे, तो दूसरे उम्मीदवार को कितने वैध वोट मिले ?
- एक शहर की जनसंख्या एक दशक में $1,75,000$ से बढ़कर $2,62,500$ हो गई । प्रति वर्ष जनसंख्या में औसत प्रतिशत वृद्धि है
