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)
- Anubhav spent 14% of his income on electricity bills, 28% on rent and 18% on shopping. If $\frac{1}{4}$ th of the remaining amount is ₹5120, how much did he spend on electricity bills ?
- The total population of a town is 50,000. The number of males and females increases by 10% and 15% respectively and consequently the population of the town becomes 56,000. What was the number of males in the town?
- Gokul donates $17\%$ of his savings to old age home, $17\%$ of the savings to orphanage and $17\%$ of his savings to foundations for medical help. The remaining amount of Rs.$9800$ of savings is been deposited in bank. Find the salary of Gokul, if $50\%$ of the salary is his savings amount. (In Rs.)
- 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?
