Growth Factor – Annual increase by one-eighth: A tree’s height increases each year by 1/8 of its current height (i.e., multiplied by 9/8 annually). If its present height is 64 cm, what will be the height after 2 years?
Aptitude
Compound Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: 81 cm
Explanation
Introduction / Context:This is a compound growth problem with multiplier 1 + 1/8 = 9/8 per year. Two years apply the multiplier twice.
Given Data / Assumptions:
- Present height H0 = 64 cm
- Annual multiplier = 9/8
- Years = 2
Concept / Approach:Future height H = H0 * (9/8)^2.
Step-by-Step Solution:(9/8)^2 = 81/64H = 64 * 81/64 = 81 cm
Verification / Alternative check:Year 1: 64 * 9/8 = 72. Year 2: 72 * 9/8 = 81.
Why Other Options Are Wrong:76, 80, 84 cm arise from simple (non-compound) additions or wrong multipliers.
Common Pitfalls:Adding 1/8 of the original each year instead of 1/8 of the current height.
Final Answer:81 cm