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Cumulative / Growth Rate DI

Introduction

Cumulative / Growth Rate Data Interpretation (DI) में data कई years या time intervals में दिया होता है, और आपका task होता है total growth, average growth या CAGR निकालना। यह pattern समझना ज़रूरी है क्योंकि real-life data जैसे company revenue, population, production आदि हमेशा time के साथ change होते हैं।

Pattern: Cumulative / Growth Rate DI

Pattern

मुख्य idea: शुरुआत और अंत के values compare करके total या annualized growth निकालना।

  • Total Growth (%) = ((Final - Initial) ÷ Initial) × 100
  • Average Growth per Year = Total Growth ÷ Number of Years
  • CAGR = [(Final ÷ Initial)1/n - 1] × 100, जहाँ n = number of years

Step-by-Step Example

Question

नीचे दी गई table में एक कंपनी की annual revenue (₹ crore में) 2020 से 2023 तक दी है। इस अवधि के लिए revenue का CAGR निकालें।

YearRevenue (₹ crore)
2020200
2021230
2022250
2023270

Solution

  1. Step 1: Initial और final values identify करें

    Initial (2020) = ₹200 crore; Final (2023) = ₹270 crore; n = 3 years

  2. Step 2: CAGR formula apply करें

    CAGR = [(270 ÷ 200)1/3 - 1] × 100 = (1.351/3 - 1) × 100 ≈ (1.104 - 1) × 100 = 10.4%

  3. Step 3: Result interpret करें

    कंपनी की revenue 2020 से 2023 के बीच औसतन 10.4% प्रति वर्ष की दर से बढ़ी।

  4. Final Answer:

    CAGR = 10.4% per annum

  5. Quick Check:

    Reverse check: 200 × (1.104)3 = 200 × 1.35 = 270 ✔️

Quick Variations

1. दो years के बीच overall percentage growth निकालना।

2. दो companies/regions का CAGR compare करना।

3. Constant growth rate देकर future value predict करना।

4. Highest cumulative growth rate वाली entity identify करना।

Trick to Always Use

  • Step 1: Base year, final year, और number of years (n) ध्यान से identify करें।
  • Step 2: Multi-year compounding हो तो हमेशा CAGR formula use करें।
  • Step 3: Result को 2 decimal places तक round करें-presentation neat रहती है।

Summary

Summary

In the Cumulative / Growth Rate DI pattern:

  • Total Growth (%) = ((Final - Initial) ÷ Initial) × 100
  • CAGR = [(Final ÷ Initial)1/n - 1] × 100
  • Time span (n) सही पकड़ना सबसे ज़रूरी है।
  • Reverse calculation से answer जल्दी verify किया जा सकता है।

Practice

(1/5)
1.

Company A - Revenue Growth (₹ crore)

The table below shows Company A’s revenue over two years. Find the total percentage growth from 2020 to 2023.

YearRevenue (₹ crore)
2020400
2023520
easy
A. 30%
B. 25%
C. 20%
D. 35%

Solution

  1. Step 1: Identify base and final values:

    Initial = ₹400 crore; Final = ₹520 crore.

  2. Step 2: Apply total growth formula:

    Growth% = ((520 - 400) ÷ 400) × 100 = (120 ÷ 400) × 100 = .

  3. Final Answer:

    30% → Option A.

  4. Quick Check:

    400 × 1.3 = 520 ✅

Hint: Subtract base from final, divide by base, and multiply by 100.
Common Mistakes: Using 2023 as base instead of 2020.
2.

City Population Growth (lakh)

The line chart shows population growth from 2016 to 2020. Find the average annual growth rate (simple growth per year).

YearPopulation (lakh)
201612
202015
easy
A. 6.25%
B. 7%
C. 7.5%
D. 8%

Solution

  1. Step 1: Compute total growth:

    Growth = 15 - 12 = 3; Total growth% = (3 ÷ 12) × 100 = 25%.

  2. Step 2: Divide by number of years:

    Years = 4 → Average = 25 ÷ 4 = .

  3. Final Answer:

    6.25% → Option A.

  4. Quick Check:

    6.25 × 4 = 25 ✅

Hint: Total growth ÷ number of years = annual growth.
Common Mistakes: Using CAGR instead of simple average growth.
3.

Firm X - Profit CAGR (₹ crore)

The bar graph shows Firm X’s profit growth. Find CAGR between 2018 and 2021.

YearProfit (₹ crore)
201810
202113.31
easy
A. 8%
B. 10%
C. 12%
D. 11%

Solution

  1. Step 1: Identify data:

    Initial = 10, Final = 13.31, n = 3.

  2. Step 2: Apply CAGR formula:

    CAGR = [(13.31 ÷ 10)1/3 - 1] × 100 = (1.3311/3 - 1) × 100 = (1.10 - 1) × 100 = .

  3. Final Answer:

    10% → Option B.

  4. Quick Check:

    10 × (1.10)3 = 13.31 ✅

Hint: Use CAGR when compounding over multiple years.
Common Mistakes: Using total growth ÷ years instead of CAGR formula.
4.

Exports Growth by Product (₹ crore)

The table shows export data for two products in two years. Which had the higher percentage growth?

Product20192022
P800960
Q600750
medium
A. Product P
B. Both equal
C. Product Q
D. Cannot determine

Solution

  1. Step 1: Calculate percentage growth:

    P: ((960 - 800) ÷ 800) × 100 = 20%.
    Q: ((750 - 600) ÷ 600) × 100 = 25%.

  2. Step 2: Compare:

    Q grew by 25%, higher than P (20%).

  3. Final Answer:

    → Option C.

  4. Quick Check:

    600 × 1.25 = 750 ✅

Hint: Compare growth% not absolute increase.
Common Mistakes: Judging by absolute numbers instead of percentages.
5.

Manufacturing Output Projection (₹ lakh)

The chart shows expected annual growth at 8% for a company starting at ₹250 lakh in 2019. Estimate its output after 3 years.

YearGrowth Rate
2019Base: ₹250 lakh
20228% p.a. compounded
medium
A. ₹310 lakh
B. ₹315 lakh
C. ₹315.8 lakh
D. ₹314.9 lakh

Solution

  1. Step 1: Use compound formula:

    Future Value = Present × (1 + r)n = 250 × (1.08)3.

  2. Step 2: Compute:

    (1.08)3 = 1.259712 → 250 × 1.259712 = ≈ ₹314.9 lakh.

  3. Final Answer:

    ₹314.9 lakh → Option D.

  4. Quick Check:

    8% compounded over 3 years ≈ 25.97% overall → 250 × 1.2597 ≈ 314.9 ✅

Hint: Use compound growth formula: Present × (1 + r)^n.
Common Mistakes: Adding simple 8% × 3 instead of compounding.

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