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Percentages, Ratios and Financial Computation PYQs for GATE DA

Solve 2+ Percentages, Ratios and Financial Computation previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

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Question 1

2025 PYQ

Level 3: Exam Standard

A rectangle has a length L and a width W, where L > W . If the width, W, is increased by 10%, which one of the following statements is correct for all values of L and W ?

Question 2

2024 PYQ

Level 3: Exam Standard

Person 1 and Person 2 invest in three mutual funds A, B, and C. The amounts they invest in each of these mutual funds are given in the table. Mutual fund A Mutual fund B Mutual fund C Person 1 ₹10,000 ₹20,000 ₹20,000 Person 2 ₹20,000 ₹15,000 ₹15,000 At the end of one year, the total amount that Person 1 gets is ₹500 more than Person 2. The annual rate of return for the mutual funds B and C is 15% each. What is the annual rate of return for the mutual fund A?

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Percentages, Ratios and Financial Computation PYQs for GATE DA

Solve 2+ Percentages, Ratios and Financial Computation previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

Chapter Roadmap: Percentages, Ratios and Financial Computation

Chapter Roadmap

Quantitative Aptitude > Numerical Computation & Estimation

1. Percentage Change in Geometry

How dimensions affect area and volume. Successive percentage changes.

2. Investment Returns & Weighted Percentages

Calculating ROI across multiple assets. Weighted averages in portfolios.

Goal: Build intuition for how proportional changes compound in shape and value.

The Non-Linear Nature of Area

Concept

The Non-Linear Nature of Area

In one dimension, a

10%

increase is linear. But in two dimensions, percentage changes compound.

A_{n e w} = L_{n e w} \times W_{n e w}

Small changes in inputs lead to larger changes in output.

Percentages, Ratios and Financial Computation: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Quantitative Aptitude · 2025 MCQ

A rectangle has a length $L$ and a width $W$ , where $L > W$ . If the width, $W$ , is increased by $10%$ , which one of the following statements is correct for all values of $L$ and $W$ ?

A.
Perimeter increases by $10%$ .
B.
Length of the diagonals increases by $10%$ .
C.
Area increases by $10%$ .
D.
The rectangle becomes a square.

Correct Answer:

Step-by-Step Solution

Insight: Area is the product of length and width; a percentage change in only one dimension translates directly to the exact same percentage change in the area, regardless of the other dimension.

Exam route: Multiply the original area by the width multiplier (1.1) to get the new area. The factor is 1.1, meaning a 10% increase.

Learning route:

Identify the original dimensions: Length = $L$ , Width = $W$ . Original Area = $L \times W$ .
Identify the change: Width is increased by 10%, so the new width is $1.1 W$ . Length remains $L$ .
Calculate the new area: $New Area = L \times 1.1 W = 1.1 L W$ .
Calculate the percentage change in area:

$\frac{1.1 L W - L W}{L W} \times 100% = 0.1 \times 100% = 10%$

Verify other options to be absolutely sure:

Perimeter: Old = $2 L + 2 W$ , New = $2 L + 2.2 W$ . Increase is $0.2 W$ , which is not 10% of $2 L + 2 W$ .
Diagonal: Old = $L^{2} + W^{2}$ , New = $L^{2} + 1.21 W^{2}$ . The increase is not a flat 10%.
Square: $L > W$ , but $1.1 W$ is not guaranteed to equal $L$ .

The correct statement is that the area increases by 10%.

Question 2 · Quantitative Aptitude · 2024 MCQ

Person 1 and Person 2 invest in three mutual funds A, B, and C. The amounts they
invest in each of these mutual funds are given in the table.

	Mutual fund A	Mutual fund B	Mutual fund C
Person 1	₹10,000	₹20,000	₹20,000
Person 2	₹20,000	₹15,000	₹15,000

At the end of one year, the total amount that Person 1 gets is ₹500 more than
Person 2. The annual rate of return for the mutual funds B and C is 15% each. What
is the annual rate of return for the mutual fund A?

A.
7.5%
B.
10%
C.
15%
D.
20%

Correct Answer:

Step-by-Step Solution

Insight: The difference in total returns between two investors with the same set of funds yields a linear equation in the unknown rate.

Exam route: Write the total return for each person using $R = \sum P_{i} r_{i}$ , subtract the two equations, and solve for $r_{A}$ .

Learning route:

Identify the rates: $r_{B} = 15% = 0.15$ , $r_{C} = 15% = 0.15$ , and let $r_{A} = r$ .
Calculate Person 1's total return:

$R_{1} = 10000 r + 20000 (0.15) + 20000 (0.15) = 10000 r + 3000 + 3000 = 10000 r + 6000$

Calculate Person 2's total return:

$R_{2} = 20000 r + 15000 (0.15) + 15000 (0.15) = 20000 r + 2250 + 2250 = 20000 r + 4500$

Use the given condition that Person 1 gets ₹500 more than Person 2:

$R_{1} - R_{2} = 500$

$(10000 r + 6000) - (20000 r + 4500) = 500$

$- 10000 r + 1500 = 500$

Solve for $r$ :

$10000 r = 1000 ⟹ r = 0.10 = 10%$

The annual rate of return for mutual fund A is 10%.

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Percentages, Ratios and Financial Computation PYQs for GATE DA

Chapter Roadmap: Percentages, Ratios and Financial Computation

Chapter Roadmap

The Non-Linear Nature of Area

The Non-Linear Nature of Area

Percentages, Ratios and Financial Computation: Solved Questions with Step-by-Step Explanations (2 Problems)

Step-by-Step Solution

Step-by-Step Solution

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