Successive Percentage Changes — Shantanu’s income is ₹ 4,000. It decreases by 10% in the first year and by 5% in the second year, but increases by 15% in the third year. What is his income at the end of the third year?

Introduction / Context:
Successive percentage changes multiply, they do not add. A decrease followed by an increase is evaluated by chaining the corresponding factors.

Given Data / Assumptions:

• Initial income = ₹ 4,000.
• Year 1: −10% ⇒ factor 0.90.
• Year 2: −5% ⇒ factor 0.95.
• Year 3: +15% ⇒ factor 1.15.

Concept / Approach:
Final income = 4,000 * 0.90 * 0.95 * 1.15.

Step-by-Step Solution:
After Year 1: 4,000 * 0.90 = 3,600After Year 2: 3,600 * 0.95 = 3,420After Year 3: 3,420 * 1.15 = 3,933

Verification / Alternative check:
The combined multiplier is 0.90 * 0.95 * 1.15 = 0.98325; 4,000 * 0.98325 = 3,933.

Why Other Options Are Wrong:
They arise from adding percentages (−10 −5 +15 = 0) which is incorrect; or from rounding at intermediate steps.

Common Pitfalls:
Adding percentage changes instead of multiplying the factors; ignoring order and compounding effect.

Final Answer:
₹ 3,933