CAT Calculating the value of a percentage change in the ratio MCQ

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Calculating the value of a percentage change in the ratio

Definition:

The percentage change in a ratio represents how much one ratio has increased or decreased in comparison to another ratio. It is an essential concept in understanding the dynamics of change, especially in business scenarios.

Formula for Percentage Change:

$\mathrm{\text { Percentage Change }=\frac{\text { New Value }- \text { Old Value }}{\text { Old Value }} \times 100 \%}$

When it's applied to ratios:

$\mathrm{\text { Percentage Change into ration}=\frac{\text { New Value }- \text { Old Value }}{\text { Old Value }} \times 100 \%}$

Foundation Building Questions:

Question:

The ratio of the number of boys to the number of girls in a class last year was 3:2. This year, the number of boys increased by 20% while the number of girls decreased by 25%. Find the new ratio and the percentage change in the ratio.

Solution:

Initial Ratio:

Boys : Girls = 3x : 2x

New Counts after Changes:

Boys = 3x X 1.20 = 3.6x (20% increase)

Girls = 2x X 0.75 = 1.5x (25% decrease)

New Ratio:

Boys : Girls = 3.6x : 1.5x

Dividing both sides by 0.3x, we get the ratio as 12:5.

Percentage Change in Ratio:

Using the formula from Concept 2 for comparing ratios,

Original ratio in terms of boys (using the unitary method from Concept 1) = 3/5 = 0.6

New ratio in terms of boys = 12/17 ≈ 0.7059

$\mathrm{\begin{aligned} & \text { Percentage Change }=\frac{0.7059-0.6}{0.6} \times 100 \% \\ & \text { PercentageChange }=17.65 \% \end{aligned}}$

Thus, the new ratio of boys to girls is 12:5, and the ratio has increased by approximately 17.65%.

Tips and Tricks:

1. Understand the Direction: Before calculating, determine whether the value is increasing or decreasing. It helps in avoiding mistakes with percentages.

2. Use the Unitary Method: As seen in the solution above, the unitary method (from Concept 1) is an efficient way to compute changes in ratios.

3. Sequential Changes: Remember that percentage changes are sequential. A 10% increase followed by a 10% decrease is not back to the original value. Always compute the absolute changes step by step.

4. Check the Whole: If you're given individual changes (like in the question above where boys increased and girls decreased), ensure that your end ratio makes sense in the context of the entire group.

5. Visualise with Bar Charts: Especially for those who are visual learners, plotting the initial and new ratios on bar charts can quickly show the magnitude and direction of change.

Regularly incorporating previous year questions in your studies ensures you're familiar with the style and depth of questions. It can give you a significant edge in competitive exams.