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Percentages, Ratios and Financial Computation Short Notes for GATE DA

Percentages, Ratios and Financial Computation short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practi

percentages ratios and financial computation short notes

Revision Checklist: Geometric Percentages

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Revision Checklist: Investment Returns

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Question 1

Level 1: Warm-up

Person 1 and Person 2 invest in two funds, A and B. Person 1 invests ₹ 10, 000 in A and ₹ 20, 000 in B. Person 2 invests ₹ 20, 000 in A and ₹ 10, 000 in B. If Person 1 gets ₹ 500 more than Person 2, and the rate of B is 10%, which of the following statements must be true?

Question 2

Level 1: Warm-up

A rectangle has area A . If its length is tripled while its width remains unchanged, which of the following must be true?

Question 3

Level 1: Warm-up

A rectangle has area A . If its length is halved while its width remains unchanged, which of the following must be true?

Question 4

Level 1: Warm-up

An investor has ₹ 100, 000 to invest in two funds: Fund X (8% return) and Fund Y (12% return). What is the maximum possible overall percentage return if at least ₹ 20, 000 must be invested in Fund X?

Question 5

Level 1: Warm-up

Person 1 invests ₹ x in Fund A (10% return) and ₹ (40, 000 - x) in Fund B (5% return). Person 2 invests ₹ (40, 000 - x) in Fund A and ₹ x in Fund B. What is the minimum value of x such that Person 1's total return is at least ₹ 500 more than Person 2's?

Question 6

Level 1: Warm-up

The length of a rectangle is increased by 100% . What is the maximum percentage by which the width can be decreased so that the area does not decrease?

Question 7

Level 1: Warm-up

The length of a rectangle is increased by 50% . What is the minimum percentage by which the width must be decreased so that the area decreases?

Question 8

Level 1: Warm-up

The length of a rectangle is increased by 50% . What is the maximum percentage by which the width can be increased so that the area increases by no more than 80% ?

Question 9

Level 1: Warm-up

The length of a rectangle is decreased by 20% . What is the minimum percentage by which the width must be increased so that the area does not decrease?

Question 10

Level 1: Warm-up

An investor puts ₹ 10, 000 in Fund A (10% return) and ₹ 40, 000 in Fund B (5% return). What is the overall percentage return?

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Percentages, Ratios and Financial Computation Short Notes for GATE DA

Percentages, Ratios and Financial Computation short notes for GATE DA: 2 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Revision Checklist: Geometric Percentages

Summary

Revision Checklist

Use Multipliers:

1 \pm \frac{p}{100}

Area Change:

M_{a r e a} = M_{L} \times M_{W}

Single Dimension: If only

W

changes by

p %

, Area changes by

p %

Compounding: Successive changes multiply.

Reversibility:

+ x %

and

- x %

results in a net decrease.

Exam Tip: Percentage change in area is independent of initial values

L

and

W

Revision Checklist: Investment Returns

Core Formulas

Total Return = \sum (P_{i} \times R_{i})

Overall Rate = \frac{Total Return}{Total Investment}

Execution Steps

Identify Weights: The investment amounts are the weights.
Set Up Equations: Write total return for each investor.
Subtract to Compare: Use differences to find relationships between rates.
Match the Target: Manipulate the relationship to match the exact expression asked in the question.

Red Flag

Never use the simple average $\frac{R _{1} + R _{2} + R _{3}}{3}$ unless the principals are equal.

Percentages, Ratios and Financial Computation: Solved Questions with Step-by-Step Explanations (10 Problems)

Question 1 · Quantitative Aptitude MCQ

Person 1 and Person 2 invest in two funds, A and B. Person 1 invests ₹ $10, 000$ in A and ₹ $20, 000$ in B. Person 2 invests ₹ $20, 000$ in A and ₹ $10, 000$ in B. If Person 1 gets ₹ $500$ more than Person 2, and the rate of B is $10%$ , which of the following statements must be true?

A.
The rate of A is $5%$ .
B.
The rate of A is $10%$ .
C.
The rate of A is $15%$ .
D.
The rate of A cannot be determined.

Correct Answer:

Step-by-Step Solution

Key idea: Use the difference in returns to find the unknown rate.

Step 1: Person 1's return = $10, 000 a + 20, 000 (0.10) = 10, 000 a + 2, 000$ .

Step 2: Person 2's return = $20, 000 a + 10, 000 (0.10) = 20, 000 a + 1, 000$ .

Step 3: Difference = $(10, 000 a + 2, 000) - (20, 000 a + 1, 000) = - 10, 000 a + 1, 000$ .

Step 4: We are given this difference is ₹ $500$ .

Step 5: $- 10, 000 a + 1, 000 = 500 ⟹ 10, 000 a = 500 ⟹ a = 0.05 = 5%$ .

Answer: The rate of A is $5%$ .

Question 2 · Quantitative Aptitude MCQ

A rectangle has area $A$ . If its length is tripled while its width remains unchanged, which of the following must be true?

A.
The new area is $A$ .
B.
The new area is $2 A$ .
C.
The new area is $3 A$ .
D.
The new area is $9 A$ .

Correct Answer:

Step-by-Step Solution

Key idea: If only one dimension changes, the area changes by the same factor as that dimension.

Step 1: Original area $A = L \times W$ .

Step 2: New length = $3 L$ , new width = $W$ .

Step 3: New area = $3 L \times W = 3 (L \times W) = 3 A$ .

Answer: The new area is $3 A$ .

Question 3 · Quantitative Aptitude MCQ

A rectangle has area $A$ . If its length is halved while its width remains unchanged, which of the following must be true?

A.
$0.25 A$
B.
$2 A$
C.
$0.5 A$
D.
$A$

Correct Answer:

Step-by-Step Solution

Key idea: If only one dimension of a rectangle changes, the area changes by the exact same factor as that dimension.

Step 1: The original area is $A = L \times W$ .

Step 2: The length is halved, so the new length is $0.5 L$ . The width remains unchanged, so the new width is $W$ .

Step 3: The new area is $0.5 L \times W = 0.5 (L \times W) = 0.5 A$ .

Answer: $0.5 A$

Question 4 · Quantitative Aptitude MCQ

An investor has ₹ $100, 000$ to invest in two funds: Fund X ( $8%$ return) and Fund Y ( $12%$ return). What is the maximum possible overall percentage return if at least ₹ $20, 000$ must be invested in Fund X?

A.
$10.4%$
B.
$11.2%$
C.
$12.0%$
D.
$9.6%$

Correct Answer:

Step-by-Step Solution

Key idea: To maximize the overall return, invest the minimum required in the lower-yielding fund and the rest in the higher-yielding fund.

Step 1: Minimum investment in Fund X ( $8%$ ) is ₹ $20, 000$ .

Step 2: Remaining investment in Fund Y ( $12%$ ) is $100, 000 - 20, 000 = ₹80, 000$ .

Step 3: Return from Fund X = $20, 000 \times 8% = ₹1, 600$ .

Step 4: Return from Fund Y = $80, 000 \times 12% = ₹9, 600$ .

Step 5: Total return = $1, 600 + 9, 600 = ₹11, 200$ .

Step 6: Overall return = $(11, 200/100, 000) \times 100% = 11.2%$ .

Answer: $11.2%$

Question 5 · Quantitative Aptitude MCQ

Person 1 invests ₹ $x$ in Fund A ( $10%$ return) and ₹ $(40, 000 - x)$ in Fund B ( $5%$ return). Person 2 invests ₹ $(40, 000 - x)$ in Fund A and ₹ $x$ in Fund B. What is the minimum value of $x$ such that Person 1's total return is at least ₹ $500$ more than Person 2's?

A.
$15, 000$
B.
$20, 000$
C.
$25, 000$
D.
$30, 000$

Correct Answer:

Step-by-Step Solution

Key idea: Set up an inequality for the difference in returns and solve for $x$ .

Step 1: Person 1's return = $0.1 x + 0.05 (40, 000 - x) = 0.05 x + 2, 000$ .

Step 2: Person 2's return = $0.1 (40, 000 - x) + 0.05 x = 4, 000 - 0.05 x$ .

Step 3: Difference = $(0.05 x + 2, 000) - (4, 000 - 0.05 x) = 0.1 x - 2, 000$ .

Step 4: We need $0.1 x - 2, 000 \geq 500$ .

Step 5: $0.1 x \geq 2, 500 ⟹ x \geq 25, 000$ .

Answer: $25, 000$

Question 6 · Quantitative Aptitude MCQ

The length of a rectangle is increased by $100%$ . What is the maximum percentage by which the width can be decreased so that the area does not decrease?

A.
25%
B.
50%
C.
75%
D.
100%

Correct Answer:

Step-by-Step Solution

Key idea: To ensure the area does not decrease, the new area must be at least the original area.

Step 1: A 100% increase in length means the new length is $2 L$ (multiplication factor = 2).

Step 2: Let the width be decreased by $x %$ . The new width is $W (1 - x /100)$ .

Step 3: For the area to not decrease: $2 L \times W (1 - x /100) \geq L \times W$ .

Step 4: Simplifying: $2 (1 - x /100) \geq 1 ⟹ 1 - x /100 \geq 0.5 ⟹ x \leq 50$ .

Step 5: The maximum percentage decrease is 50%.

Answer: 50%

Question 7 · Quantitative Aptitude MCQ

The length of a rectangle is increased by $50%$ . What is the minimum percentage by which the width must be decreased so that the area decreases?

A.
33.33%
B.
25%
C.
50%
D.
66.67%

Correct Answer:

Step-by-Step Solution

Key idea: For the area to decrease, the area multiplication factor must be less than 1.

Step 1: Length increase of 50% means $M_{L} = 1.5$ .

Step 2: Let width be decreased by $x %$ . Then $M_{W} = 1 - x /100$ .

Step 3: For area to decrease: $M_{L} \times M_{W} < 1 ⟹ 1.5 \times (1 - x /100) < 1$ .

Step 4: $1 - x /100 < 2/3 ⟹ x /100 > 1/3 ⟹ x > 33.33$ .

Step 5: The minimum percentage decrease is approximately 33.33%.

Answer: 33.33%

Question 8 · Quantitative Aptitude MCQ

The length of a rectangle is increased by $50%$ . What is the maximum percentage by which the width can be increased so that the area increases by no more than $80%$ ?

A.
$20%$
B.
$30%$
C.
$50%$
D.
$80%$

Correct Answer:

Step-by-Step Solution

Key idea: To find the maximum percentage increase in width, set the new area to the maximum allowed value and solve for the width multiplier.

Step 1: The length multiplier is $1 + 50/100 = 1.5$ .

Step 2: Let the width multiplier be $M_{W}$ . The area multiplier is $1.5 \times M_{W}$ .

Step 3: The area increases by no more than 80%, so the area multiplier is at most $1.8$ .

Step 4: $1.5 \times M_{W} = 1.8 ⟹ M_{W} = 1.2$ .

Step 5: The width multiplier of 1.2 corresponds to a 20% increase.

Answer: $20%$

Question 9 · Quantitative Aptitude MCQ

The length of a rectangle is decreased by $20%$ . What is the minimum percentage by which the width must be increased so that the area does not decrease?

A.
$20%$
B.
$25%$
C.
$30%$
D.
$40%$

Correct Answer:

Step-by-Step Solution

Key idea: To ensure the area does not decrease, the product of the length and width multipliers must be at least 1.

Step 1: The length is decreased by 20%, so the length multiplier is $1 - 20/100 = 0.8$ .

Step 2: Let the width multiplier be $M_{W}$ . The area multiplier is $0.8 \times M_{W}$ .

Step 3: For the area to not decrease, $0.8 \times M_{W} \geq 1 ⟹ M_{W} \geq 1.25$ .

Step 4: A width multiplier of 1.25 corresponds to a 25% increase.

Step 5: The minimum percentage increase in width is 25%.

Answer: $25%$

Question 10 · Quantitative Aptitude NAT

An investor puts ₹ $10, 000$ in Fund A ( $10%$ return) and ₹ $40, 000$ in Fund B ( $5%$ return). What is the overall percentage return?

Correct Answer:

6.00

Step-by-Step Solution

Key idea: The overall return is the weighted average of the individual returns, weighted by the investment amounts.

Step 1: Return from Fund A = $10, 000 \times 10% = ₹1, 000$ .

Step 2: Return from Fund B = $40, 000 \times 5% = ₹2, 000$ .

Step 3: Total return = $1, 000 + 2, 000 = ₹3, 000$ .

Step 4: Total investment = $10, 000 + 40, 000 = ₹50, 000$ .

Step 5: Overall percentage return = $(3, 000/50, 000) \times 100% = 6%$ .

Answer: 6.00

percentages ratios and financial computation short notes

Revision Checklist: Geometric Percentages

Revision Checklist

Revision Checklist: Investment Returns

Revision Checklist: Investment Returns

Try a question

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Personalised first. High quality throughout.

Built around you, not around a syllabus PDF

Revision that hits your weak spots

Questions calibrated to the real exam

Notes written for recall, not for volume

One place for everything

Honest progress

Unlock the whole course

Percentages, Ratios and Financial Computation Short Notes for GATE DA

Revision Checklist: Geometric Percentages

Revision Checklist

Revision Checklist: Investment Returns

Revision Checklist: Investment Returns

Percentages, Ratios and Financial Computation: Solved Questions with Step-by-Step Explanations (10 Problems)

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

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