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Ratio & Percentage Based DI

Introduction

Ratio और percentage वाले problems Data Interpretation में सबसे basic और सबसे ज़्यादा पूछे जाने वाले topics हैं। ये parts को आपस में या पूरे से compare करने में मदद करते हैं। ऐसे questions exams और real-world analysis (market share, ingredient mix, finance split) दोनों में बहुत common होते हैं। इनका mastery आपको ratios और percentages के बीच जल्दी conversion करने और totals पर percentage apply करने में मदद करता है।

Pattern: Ratio & Percentage Based DI

Pattern

Key concept: Ratio parts को compare करता है, percentage = (part ÷ whole) × 100. Ratio और percentage के बीच convert करना और सही base पर percentage apply करना सबसे महत्वपूर्ण step है।

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

Step-by-Step Example

Question

एक कंपनी की revenue तीन products A, B, C के बीच 3 : 4 : 5 ratio में बंटी है। अगर total annual revenue ₹12,00,000 है, तो product B की revenue निकालें।

Solution

  1. Step 1: Ratio और total parts समझें

    A : B : C = 3 : 4 : 5 → Total parts = 3 + 4 + 5 = 12 parts

  2. Step 2: One part का value निकालें

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

  3. Step 3: B का हिस्सा निकालें

    B = 4 parts = 4 × 1,00,000 = ₹4,00,000

  4. Final Answer:

    ₹4,00,000

  5. Quick Check:

    3,00,000 + 4,00,000 + 5,00,000 = ₹12,00,000 ✔️

Quick Variations

1. Ratio दिया है, एक part missing है - total से missing part निकालें।

2. Percentage increase/decrease - percent को multiplier (1 ± R/100) में convert करें।

3. Ratio को percentage में convert करना या percentage को ratio में (total parts का उपयोग करके)।

4. Mixed units (thousands, lakhs) - calculation से पहले units standardize करें।

Trick to Always Use

  • Step 1 → Ratio numbers को पहले add करें और total parts निकालें।
  • Step 2 → One-part value = Total ÷ Total parts (units का ध्यान रखें)।
  • Step 3 → One-part value को required ratio part से multiply करें, या percentage का formula इस्तेमाल करें।

Summary

Summary

In the Ratio & Percentage Based DI pattern:

  • Calculation से पहले ratio को total parts में convert करें।
  • (percent × total) ÷ 100 का formula हमेशा correct base के साथ apply करें।
  • Units (thousands, lakhs, crores) consistent रखें।
  • Answer verify करने के लिए parts को वापस add करें या percentage re-check करें।

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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