### Chapter 14 Compound Interest – Exercise 14.4 | Set 1

**Question 11. 6400 workers were employed to construct a river bridge in four years. At the end of the first year, 25% workers were retrenched. At the end of the second year, 25% of those working at that time were retrenched. However, to complete the project in time, the number of workers was increased by 25% at the end of the third year. How many workers were working during the fourth year?**

**Solution:**

We have,

Initial number of workers are = 6400

At the end of first year = 25% retrenched

At the end of second year = 25% retrenched

At the end of third year = 25% increased

By using the formula,

A = P (1 + )

Substituting the values, we have

x = 6400 (1 – ) (1 – ) (1 + )

= 6400 () () ()

= 6400 (0.75) (0.75) (1.25)

= 4500

Therefore,

Number of workers working during the fourth year is 4500.

**Question 12. Aman started a factory with an initial investment of Rs 100000. In the first year, he incurred a loss of 5%. However, during the second year, he earned a profit of 10% which in the third year rose to 12%. Calculate his net profit for the entire period of three years.**

**Solution:**

We have,

Initial investment by Aman = Rs.100000

In first year = incurred a loss of 5%

In second year = earned a profit of 10%

In third year = earned a profit of 12 %

By using the formula,

A = P (1 + )

Substituting the values, we have

x = 100000 (1 – ) (1 + ) (1 + )

= 100000 () () ()

= 100000 (0.95) (1.1) (1.12)

= 117040

Therefore,

Aman’s net profit for entire three years is 117040 – 100000 = Rs 17040.

**Question 13. The population of a town increases at the rate of 40 per thousand annually. If the present population be 175760, what was the population three years ago.**

**Solution:**

We have,

Annul increase rate of population of town = 40/1000× 100 = 4%

Present population of town = 175760

So, let the population of town 3 years ago be = x

By using the formula,

A = P (1 + )

Substituting the values, we have

175760 = x (1 + ) (1 + ) (1 + )

175760 = x () ( (

175760 = x (1.04) (1.04) (1.04)

175760 = 1.124864x

x = 175760/1.124864

= 156250

Therefore,

Population 3 years ago was 156250.

**Question 14. The population of a mixi company in 1996 was 8000 mixies. Due to increase in demand it increases its production by 15% in the next two years and after two years its demand decreases by 5%. What will its production after 3 years?**

**Solution:**

We have,

Population of mixi company in 1996 was = 8000 mixies

Production growth rate in next 2 years is = 15 %

Decrease rate in 3rd year is = 5%

By using the formula,

A = P (1 + )

Substituting the values, we have

x = 8000 (1 + ) (1 + ) (1 – )

= 8000 (0) () ()

= 8000 (1.15) (1.15) (0.95)

= 10051

Therefore,

Production after three years will be 10051 mixies.

**Question 15. The population of a city increases each year by 4% of what it had been at the beginning of each year. If the population in 1999 had been 6760000, find the population of the city in (1) 2001 (ii) 1997.**

**Solution:**

We have,

Annual increase rate of population of city is = 4%

Population in 1999 was = 6760000

(i) Population of the city in 2001 (2 years after)

By using the formula,

A = P (1 + )

Substituting the values, we have

x = 6760000 (1 + ) (1 + )

= 6760000 () ()

= 6760000 (1.04) (1.04)

= 7311616

Therefore,

Population in the year 2001 is 7311616

(ii) Population of city in 1997 (2 years ago)

By using the formula,

A = P (1 + )

Substituting the values, we have

x = 6760000 (1 – ) (1 – )

= 6760000 () ()

= 6760000 (0.96) (0.96)

= 6230016

Therefore,

Population in the year 1997 was 6230016.

**Question 16. Jitendra set up a factory by investing Rs. 2500000. During the first two successive years his profits were 5% and 10% respectively. If each year the profit was on previous year’s capital, compute his total profit.**

**Solution:**

We have,

Initial investment by Jitendra was = Rs 2500000

Profit in first 2 successive years were = 5% and 10%

Final investment after two successive profits = 2500000 (1 + ) (1 + )

= 2500000 () ()

= 2500000 (1.05) (1.1)

= 2887500

Therefore,

Jitendra total profit is = 2887500 – 2500000 = Rs 387500.