The ratio of the students in schools $A, B$ and $C$ is 5 : 4 : 7. If the number of students in the schools are increased by 20%, 25% and 20% respectively, what would be the new ratio of the students in schools $A, B$ and $C$? (Bank P.O., 2010)

### Concept & Percentage Increase in Ratios To find the new ratio after each part of a ratio undergoes a percentage increase, multiply the original ratio parts by their respective growth factors $(1 + \frac{r}{100})$. ### Step-by-Step Solution * **Assume Initial Values**: Let the number of students in schools $A, B$, and $C$ be $5x$, $4x$, and $7x$. To make percentage calculations easy, assume $x = 10$. So, the initial students are $50$, $40$, and $70$. * **Calculate Increases**: * School $A$ new students = $50 \times (1 + \frac{20}{100}) = 50 \times 1.20 = 60$. * School $B$ new students = $40 \times (1 + \frac{25}{100}) = 40 \times 1.25 = 50$. * School $C$ new students = $70 \times (1 + \frac{20}{100}) = 70 \times 1.20 = 84$. * **Find the New Ratio**: New Ratio = $60 : 50 : 84$. * **Simplify**: Divide all terms by $2$. New Ratio = $30 : 25 : 42$. ### Exam Strategy & Shortcut Skip the variables and multiply the ratio numbers directly by their percentage multipliers: $A = 5 \times 1.2 = 6$ $B = 4 \times 1.25 = 5$ $C = 7 \times 1.2 = 8.4$ Ratio = $6 : 5 : 8.4$. Multiply by $10$ to remove the decimal $\implies 60 : 50 : 84$. Simplify by dividing by $2 \implies 30 : 25 : 42$. ### Common Pitfall Trying to add the percentages directly to the ratio values (e.g., $5 + 0.20 = 5.20$) instead of applying the percentage as a multiplier of the base ratio unit. ### Final Answer Therefore, the correct answer is **30 : 25 : 42**.