How to Solve: CUET Quant – Ratio, Percentage, Average & Partnership

How to Solve: CUET Quant – Ratio, Percentage, Average & Partnership

Introduction

"Imagine you’re running a startup with three partners. How do you split profits fairly? Or, in your exam, how do you solve a 5-mark question in under 2 minutes? Master ratios, percentages, averages, and partnerships—this is the toolkit that unlocks both."

What You Need To Know First

1. Basic arithmetic operations (addition, subtraction, multiplication, division).
2. Fractions and decimals (converting between them).
3. Unitary method (finding value of one unit to solve for many).

Key Vocabulary

Formulas To Know

1. Ratio Simplification & Division

Formula: If a ratio is given as a : b, and a total amount T is to be divided in this ratio: - Part for A = (a / (a + b)) × T - Part for B = (b / (a + b)) × T

Variables: - a, b = terms of the ratio. - T = total amount to be divided.

Memorise This.

2. Percentage Change

Formula: Percentage Change = [(New Value – Old Value) / Old Value] × 100

Variables: - New Value = Updated quantity. - Old Value = Original quantity.

Memorise This.

3. Average (Mean)

Formula: Average = (Sum of all values) / (Number of values)

Variables: - Sum of all values = Total of all data points. - Number of values = Count of data points.

Memorise This.

4. Weighted Average

Formula: Weighted Average = (Σ (Value × Weight)) / (Σ Weights)

Variables: - Value = Individual data point. - Weight = Importance/weight of that data point.

Memorise This.

5. Partnership Profit Sharing (Simple Ratio)

Formula: If A : B = a : b, then: - A’s share = (a / (a + b)) × Total Profit - B’s share = (b / (a + b)) × Total Profit

Memorise This.

6. Partnership Profit Sharing (Time-Weighted Ratio)

Formula: If A invests ₹P₁ for T₁ months and B invests ₹P₂ for T₂ months, then: Profit Sharing Ratio = (P₁ × T₁) : (P₂ × T₂)

Memorise This.

Step-by-Step Method

Step 1: Understand the Problem

• Read the question twice.
• Identify what is given (ratios, percentages, investments, time).
• Identify what is asked (profit share, average, percentage change).

Step 2: Convert All Data to the Same Form

• If percentages are given, convert to decimals (e.g., 20% = 0.20).
• If ratios are given, simplify them (e.g., 4:6 → 2:3).
• If time is given in months, keep it consistent (don’t mix years and months).

Step 3: Apply the Correct Formula

• Ratio division? Use a/(a+b) × T.
• Percentage change? Use [(New – Old)/Old] × 100.
• Average? Use Sum/Count.
• Partnership? Use (P₁ × T₁) : (P₂ × T₂).

Step 4: Solve Step-by-Step

• Break the problem into smaller parts.
• Solve one part at a time (e.g., first find ratio, then apply to profit).
• Double-check calculations (especially percentages and ratios).

Step 5: Verify the Answer

• Does the answer make sense? (e.g., profit shares should add up to total profit).
• If stuck, plug in numbers to test (e.g., assume total profit = ₹100).

Worked Example (Using Steps Above)

Question: A and B invest in a business in the ratio 3:5. After 1 year, the business earns a profit of ₹40,000. What is A’s share?

Solution: 1. Understand: Given ratio = 3:5, total profit = ₹40,000. Asked: A’s share. 2. Convert: Ratio is already simplified (3:5). 3. Formula: Use a/(a+b) × T → A’s share = (3 / (3+5)) × 40,000. 4. Solve:
- 3 + 5 = 8
- A’s share = (3/8) × 40,000 = ₹15,000 5. Verify: B’s share = (5/8) × 40,000 = ₹25,000. Total = 15,000 + 25,000 = ₹40,000 ✔

Answer: ₹15,000

Worked Examples

Example 1 – Basic (Ratio & Percentage)

Question: The ratio of boys to girls in a class is 4:5. If there are 36 girls, how many boys are there? Also, what percentage of the class are boys?

Solution: 1. Understand: Ratio = 4:5 (boys:girls), girls = 36. Find boys and % boys. 2. Convert: Ratio is simplified. Girls = 5 parts = 36. 3. Find 1 part: 1 part = 36 / 5 = 7.2 4. Boys = 4 parts: 4 × 7.2 = 28.8 → Since students can’t be in decimals, assume 29 boys (rounding). 5. Total students: 29 + 36 = 65 6. % boys: (29 / 65) × 100 ≈ 44.62%

What we did and why: - Used ratio to find parts → converted to actual numbers. - Calculated percentage using (part/whole) × 100.

Example 2 – Medium (Average & Partnership)

Question: Three friends, A, B, and C, invest ₹2000, ₹3000, and ₹5000 respectively in a business. After 1 year, the profit is ₹10,000. If A invested for 6 months, B for 12 months, and C for 8 months, what is C’s share?

Solution: 1. Understand: Investments = ₹2000, ₹3000, ₹5000. Time = 6, 12, 8 months. Profit = ₹10,000. 2. Convert: Use time-weighted ratio → (P × T). 3. Calculate ratio:
- A = 2000 × 6 = 12,000
- B = 3000 × 12 = 36,000
- C = 5000 × 8 = 40,000
- Ratio = 12 : 36 : 40 → Simplify by dividing by 4 → 3 : 9 : 10 4. Total parts: 3 + 9 + 10 = 22 5. C’s share: (10 / 22) × 10,000 ≈ ₹4,545.45

What we did and why: - Adjusted for time (not just investment). - Simplified ratio to make calculations easier.

Example 3 – Exam Style (Disguised Problem)

Question: A shopkeeper sells two types of rice. The ratio of the cost price of Type A to Type B is 3:4. The selling price of Type A is 20% above cost price, and Type B is sold at 10% profit. If the total selling price is ₹2800, find the cost price of Type A.

Solution: 1. Understand: CP ratio = 3:4. SP of A = 120% of CP, SP of B = 110% of CP. Total SP = ₹2800. 2. Let CP of A = 3x, CP of B = 4x (from ratio). 3. SP of A = 1.2 × 3x = 3.6x 4. SP of B = 1.1 × 4x = 4.4x 5. Total SP = 3.6x + 4.4x = 8x = ₹2800 6. Solve for x: x = 2800 / 8 = 350 7. CP of A = 3x = 3 × 350 = ₹1050

What we did and why: - Assigned variables (3x, 4x) to simplify ratio. - Used percentage profit to find SP in terms of x. - Solved for x and substituted back.

Common Mistakes

Exam Traps

1-Minute Recap

"Alright, let’s lock this in—last-minute checklist for CUET Quant: Ratio, Percentage, Average, Partnership.

1. Ratios: Simplify first, then divide the total using a/(a+b) × T.
2. Percentages: Always use [(New – Old)/Old] × 100. If it’s a profit, add to 100%; if loss, subtract.
3. Averages: Sum divided by count. If weighted, multiply each value by its weight first.
4. Partnerships: Investment × Time is your ratio. If time isn’t given, assume equal.
5. Watch for traps: Time in partnerships, hidden percentages, missing data in averages.

Do 3 problems tonight—one ratio, one percentage, one partnership. Time yourself: 2 minutes per question. You’ve got this!