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Ratio & Percentage Based DI

Introduction

Ratio and percentage problems are foundational in Data Interpretation - they help compare parts to each other and to the whole. These questions appear frequently in exams and real-world analysis (market share, ingredient mixes, finance splits). Mastering them lets you convert between ratios and percentages and apply percentages to totals quickly.

Pattern: Ratio & Percentage Based DI

Pattern

Key concept: Convert between ratios and percentages, and apply percentage formulas to the correct base. Ratios compare parts; percentage = (part ÷ whole) × 100.

Useful formulas:
Percentage of total: Value = (Percent × Total) ÷ 100.
Percent from ratio: Percent = (Part ÷ Whole) × 100.
Converting ratio to share: If ratio = a:b:c and total = T, then part a = (a ÷ (a+b+c)) × T.

Step-by-Step Example

Question

A company's revenue is split among three products A, B and C in the ratio 3:4:5. If the total annual revenue is ₹12,00,000, find the revenue from product B.

Solution

  1. Step 1: Understand the ratio and total parts:

    The ratio A:B:C = 3 : 4 : 5. Total parts = 3 + 4 + 5 = 12 parts.

  2. Step 2: Find value of one part:

    One part = Total revenue ÷ Total parts = 12,00,000 ÷ 12 = ₹1,00,000.

  3. Step 3: Compute B's revenue:

    B's share = 4 parts = 4 × 1,00,000 = ₹4,00,000.

  4. Final Answer:

    ₹4,00,000

  5. Quick Check:

    Sum of parts: 3×1,00,000 + 4×1,00,000 + 5×1,00,000 = 3,00,000 + 4,00,000 + 5,00,000 = ₹12,00,000 ✅

Quick Variations

1. Ratio given, one part missing - find the missing part using total.

2. Percentage of increase/decrease applied to a base - convert percent to multiplier (1 ± R/100).

3. Convert ratio to percentage shares and vice versa (use total parts or multiply by 100).

4. Mixed units: ratios applied to totals expressed in thousands/lakhs - convert units consistently.

Trick to Always Use

  • Step 1 → Write total parts clearly: add the ratio numbers first.
  • Step 2 → Compute one-part value by dividing the total by total parts (keep units consistent).
  • Step 3 → Multiply the one-part value by the required ratio portion or apply percent formula as needed.

Summary

Summary

In the Ratio & Percentage Based DI pattern:

  • Always convert ratios into total parts before calculation.
  • Use (percent × total) ÷ 100 to find values based on percentage.
  • Keep units consistent - thousands, lakhs, or crores - before comparing or summing values.
  • Verify results by re-summing parts or recalculating the overall percentage for accuracy.

Practice

(1/5)
1.

School Expenditure Breakdown

The table shows the yearly expenditure (in ₹ lakh) of a school under different heads. What percentage of total expenditure was spent on Staff Salaries?

CategoryAmount (₹ lakh)
Staff Salaries80
Infrastructure40
Maintenance20
Miscellaneous10
easy
A. 50%
B. 52%
C. 54%
D. 53%

Solution

  1. Step 1: Calculate the total expenditure:

    Total expenditure = 80 + 40 + 20 + 10 = 150 (₹ lakh).

  2. Step 2: Find the share of staff salaries:

    Percentage spent on salaries = (80 ÷ 150) × 100 = 53.33%.

  3. Step 3: Round to nearest integer:

    Rounded value = 53%.

  4. Final Answer:

    53% → Option D.

  5. Quick Check:

    80 ÷ 150 = 0.533 → 53% ✅

Hint: To find a category’s percentage, divide its value by the total and multiply by 100.
Common Mistakes: Using incorrect total or rounding too early in the calculation.
2.

Product Revenue Mix

The table shows the percentage contribution of four products to the total revenue of a company. If total revenue is ₹2,000,000, find the revenue from Product B.

ProductRevenue %
A25%
B30%
C20%
D25%
easy
A. ₹400,000
B. ₹600,000
C. ₹500,000
D. ₹700,000

Solution

  1. Step 1: Identify total and percentage:

    Total revenue = ₹2,000,000; Product B = 30%.

  2. Step 2: Apply percentage formula:

    Revenue(B) = (30 × 2,000,000) ÷ 100 = .

  3. Final Answer:

    ₹600,000 → Option B.

  4. Quick Check:

    0.30 × 2,000,000 = 600,000 ✅

Hint: Multiply total by (percent ÷ 100).
Common Mistakes: Using wrong percentage or forgetting to divide by 100.
3.

Population Gender Ratio

The table shows population distribution in a town. Find the number of males if total population is 50,000.

GenderRatio
Male3
Female2
easy
A. 30,000
B. 25,000
C. 20,000
D. 15,000

Solution

  1. Step 1: Sum ratio parts:

    3 + 2 = .

  2. Step 2: Value per part:

    One part = 50,000 ÷ 5 = 10,000.

  3. Step 3: Compute males:

    Males = 3 × 10,000 = 30,000.

  4. Final Answer:

    30,000 → Option A.

  5. Quick Check:

    30,000 : 20,000 = 3 : 2 and sum = 50,000 ✅

Hint: Find one part by dividing total by sum of parts, then multiply.
Common Mistakes: Using ratio parts incorrectly or reversing order.
4.

Department Salary Comparison

The table shows average salaries of employees in two departments. What is the ratio of average salary of Dept. X to Dept. Y?

DepartmentAverage Salary (₹)
X60,000
Y50,000
medium
A. 6:5
B. 5:6
C. 7:5
D. 4:5

Solution

  1. Step 1: Form the ratio:

    Ratio = 60,000 : 50,000.

  2. Step 2: Simplify:

    Divide both numbers by 10,000 → .

  3. Final Answer:

    6:5 → Option A.

  4. Quick Check:

    60k ÷ 50k = 1.2 = 6/5 ✅

Hint: Always simplify ratio to lowest whole-number terms.
Common Mistakes: Inverting the ratio or not simplifying correctly.
5.

Company Investment & Return %

The table shows investments and return rates for two companies. Find total return (₹ lakh).

CompanyInvestment (₹ lakh)Return %
A4015%
B6010%
medium
A. ₹10 lakh
B. ₹11 lakh
C. ₹12 lakh
D. ₹10.5 lakh

Solution

  1. Step 1: Compute returns per company:

    A's return = (15% of 40) = (15 × 40) ÷ 100 = .
    B's return = (10% of 60) = (10 × 60) ÷ 100 = 6 lakh.

  2. Step 2: Total return:

    Total = 6 + 6 = ₹12 lakh.

  3. Final Answer:

    ₹12 lakh → Option C.

  4. Quick Check:

    6 + 6 = 12 ✅

Hint: Compute (return% × investment) ÷ 100 for each, then add.
Common Mistakes: Averaging percentages instead of computing actual amounts.

Mock Test

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