CAPF AC 2021 Q54: General Mental Ability – Quantitative Aptitude
A tree is at present 9 feet tall. If every year it grows 1⁄9 of its height, what will be the height of the tree after three years?
- (a) 12 feet
- (b) 12·34 feet
- (c) 13 feet
- (d) 13·10 feet
Answer: (b) 12·34 feet
Explanation
Height of a growing tree
Given: a tree is at present 9 feet tall and every year it grows 1⁄9 of its height; find its height after three years.
How to think: the growth is on the new height each year.
This is compound growth, like compound interest.
Each year the height becomes 1 + 1/9 = 10/9 times.
| Year | Working | Height |
|---|---|---|
| Start | Given | 9 feet |
| After 1 year | 9 × 10/9 | 10 feet |
| After 2 years | 10 × 10/9 | 11.11 feet |
| After 3 years | 11.11 × 10/9 | 12.34 feet |
In one line: 9 × (10/9)³ = 1000/81 = 12.34 feet (approximately).
Answer: (b) 12·34 feet.
Why each option is right or wrong
- (a) Incorrect. 12 feet is simple growth: 1 foot a year for three years.
- (b) CORRECT. 9 × (10/9)³ = 1000/81, which is about 12.34 feet.
- (c) Incorrect. 13 feet is more than three years of compound growth gives.
- (d) Incorrect. 13.10 feet does not come from any correct working.
Key point
Growth on the current value each year is compound growth: final = initial × (1 + rate)^years. Here 9 × (10/9)³ = 1000/81 ≈ 12.34.
Remember
Grows a fraction of its height each year = compound growth.
Common mistakes
- Adding a fixed 1 foot every year and getting 12 feet.
- Forgetting that each year's growth is on the new height, not the first height.
- Rounding too early and landing on 13 feet instead of 12.34 feet.
Exam tip
Educated guess: simple growth gives exactly 12 feet. Compound growth must be a little more than 12, and 12.34 is the only option just above it.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (compound interest and growth)
- R. S. Aggarwal, Quantitative Aptitude — Compound Interest