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:
10 : 12 : 15
Understanding the Problem: Ratio and Percentage Increase
The problem asks us to find the new ratio of students in three classes after their initial numbers, which are in a given ratio, increase by specific percentages.
Initially, the numbers of students in the three classes are in the ratio 4 : 5 : 6.
This means if the number of students in the first class is $4x$, then the number of students in the second class is $5x$, and in the third class is $6x$, for some common factor $x$.
Calculating the Increase in Each Class
The number of students in each class increases by a certain percentage:
- Class 1: Increase by 25%
- Class 2: Increase by 20%
- Class 3: Increase by 25%
Finding the New Number of Students
To find the new number of students in each class, we add the percentage increase to the original number.
An increase of P% means the new value is the original value plus P% of the original value, which can be written as: New Value = Original Value $\times (1 + \frac{P}{100})$.
Let's calculate the new number of students for each class:
- Class 1: Original number = $4x$. Increase = 25%. New number = $4x \times (1 + \frac{25}{100}) = 4x \times (1 + 0.25) = 4x \times 1.25$. $\qquad 4 \times 1.25 = 5$. So, new number of students in Class 1 is $5x$.
- Class 2: Original number = $5x$. Increase = 20%. New number = $5x \times (1 + \frac{20}{100}) = 5x \times (1 + 0.20) = 5x \times 1.20$. $\qquad 5 \times 1.20 = 6$. So, new number of students in Class 2 is $6x$.
- Class 3: Original number = $6x$. Increase = 25%. New number = $6x \times (1 + \frac{25}{100}) = 6x \times (1 + 0.25) = 6x \times 1.25$. $\qquad 6 \times 1.25 = 7.5$. So, new number of students in Class 3 is $7.5x$.
Determining the New Ratio
The new numbers of students in the three classes are $5x$, $6x$, and $7.5x$.
The new ratio is the ratio of these new numbers:
New Ratio = $5x : 6x : 7.5x$
Simplifying the New Ratio
To simplify the ratio, we can divide each term by the common factor $x$ (assuming $x \neq 0$).
Ratio = $5 : 6 : 7.5$
To express the ratio with whole numbers, we can multiply each term by a suitable number to remove the decimal. Multiplying by 2 will remove the decimal in 7.5:
$5 \times 2 : 6 \times 2 : 7.5 \times 2$
$10 : 12 : 15$
The new ratio of the numbers of students in the three classes is 10 : 12 : 15.
Important Questions from Percentage
A batsman scored 160 runs in a cricket match. He hit 24 fours and 8 sixes during his innings. What percentage of his runs were in boundaries?
Mohan's income is 40% more than Shyam's income. Shyam's income is what percentage less than Mohan's income?
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 ?
