A machine depreciates at the rate of 10% of its value at the beginning of a year. If the present value of a machine is ₹ 8,000, its value after 3 years will be:

1. ₹ 5,382

2. ₹ 5,832

3. ₹ 5,238

4. ₹ 5,638

The present population of a town is 200000. The population will increase by 10% in the first year and 15% in the second year. The population of the town after two years will be:

1. 253000

2. 235000

3. 203500

4. 352000

The value of a machine depreciates every year at a constant rate. If the values of the machine in 2006 and 2008 are ₹ 25,000 and ₹ 19,360 respectively, then the annual rate of depreciation is:

1. 8%

2. 10%

3. 12%

4. 14%

Case Study

In 2015, the population of a town was 20000. During 2016 and 2017, it increases by 4% and 5% every year respectively. In 2018, due to an epidemic and migration to cities, the population decreases at 5%. Based on the above information answer the following questions:

1. The population of the town in 2016 was:
   (a) 20800
   (b) 20500
   (c) 20460
   (d) 20300

2. The difference in the population of the town at the end of the years 2017 and 2015 was:
   (a) 1500
   (b) 1700
   (c) 1800
   (d) 1840

3. The population of the town at the end of the year 2018 was:
   (a) 20100
   (b) 20500
   (c) 20748
   (d) 20850

4. Which of the following expressions gives the population at the end of the year 2018?
   
   (a) $20000 \times \dfrac{104}{100} \times \dfrac{105}{100} \times \dfrac{105}{100}$
   
   (b) $20000 \times \dfrac{104}{100} \times \dfrac{105}{100} \times \dfrac{95}{100}$
   
   (c) $20000 \times \dfrac{104}{100} \times \dfrac{95}{100}\times \dfrac{95}{100}$
   
   (d) $20000 \times \dfrac{96}{100} \times \dfrac{95}{100} \times \dfrac{95}{100}$

5. If the population of the town at the end of 2019 was 21,163, then during 2019, the population increases at the rate of:
   (a) 2%
   (b) 3%
   (c) 3.5% (d) 4%