Quants Questions for CLAT | QB Set 19 – Growth and Decay Problems 

A city administration launched an environmental project to monitor tree growth and groundwater levels over five years. According to the report, a newly planted forest had 20,000 saplings, and the number of healthy trees increased by 10% every year because of proper care and irrigation. 

At the same time, a nearby water reservoir contained 5,00,000 litres of water, but due to evaporation and regular usage, its water level decreased by 8% every year. In another part of the city, an old warehouse stored 8,000 kilograms of grain, which naturally decayed at the rate of 15% every year because of poor storage conditions. The administration also monitored a wildlife reserve where the deer population was 2,500, increasing by 12% annually due to conservation efforts. 

Officials used these figures to estimate future resource requirements, evaluate sustainability measures, and plan new conservation strategies. They relied on the principles of compound growth and compound decay, where every year’s increase or decrease was calculated on the value obtained at the end of the previous year rather than on the original amount.

Questions

Q1. The number of healthy trees grows by 10% every year. Approximately how many healthy trees will there be after 2 years?

A. 24,200

B. 22,000

C. 23,500

D. 24,000

Q2. The reservoir initially contains 5,00,000 litres of water and loses 8% every year. Approximately how much water will remain after 3 years?

A. 4,00,000 litres

B. 3,95,000 litres

C. 3,80,000 litres

D. 3,89,344 litres

Q3. The warehouse stores 8,000 kg of grain, which decays by 15% annually. Approximately how much grain remains after 2 years?

A. 6,200 kg

B. 5,780 kg

C. 6,000 kg

D. 5,500 kg

Q4. The deer population increases by 12% annually. What will be the approximate deer population after 1 year?

A. 2,700

B. 2,750

C. 2,800

D. 3,000

Q5. If an investment grows at 20% per year, what will be the value of ₹50,000 after 2 years?

A. ₹72,000

B. ₹70,000

C. ₹68,000

D. ₹75,000

Answers with Detailed Explanation

Q1. Answer: A

20,000 × (1.10)^2 = 20,000 × 1.21 = 24,200.

Q2. Answer: D

5,00,000 × (0.92)^3 = 5,00,000 × 0.778688 = 3,89,344 litres.

Q3. Answer: B

8,000 × (0.85)^2 = 8,000 × 0.7225 = 5,780 kg.

Q4. Answer: C

2,500 × 1.12 = 2,800.

Q5. Answer: A

50,000 × (1.20)^2 = 50,000 × 1.44 = ₹72,000.