A papaya tree grows by 20% every year. Two years later its height is 540 cm. What was its height when planted (2 years ago)?

Introduction / Context:
This is reverse compound growth. If a quantity grows by a fixed percentage each year, its current value equals initial value times the compounded growth factor. To find the initial value, divide the current value by that factor.

Given Data / Assumptions:

• Annual growth = 20% ⇒ factor 1.20 each year.
• Elapsed time = 2 years.
• Current height = 540 cm.

Concept / Approach:
If H₀ is initial height, then present height H = H₀ * (1.20)^2. Therefore, H₀ = H / (1.20^2).

Step-by-Step Solution:

Verification / Alternative check:
Grow 375 by 20% twice: Year 1 → 375 * 1.2 = 450; Year 2 → 450 * 1.2 = 540. Matches.

Why Other Options Are Wrong:
324 and 432 reflect using 10% or 15% instead of 20% or mixing up square vs double counting.

Common Pitfalls:
Subtracting 2*20% from 540 or dividing by (1 + 2*0.2) instead of squaring the growth factor.

Final Answer:
375 cms