**Chapter 8 Comparing Quantities Exercise 8.3**

Solution:

(a) Given:

P = ₹ 10,800, n = 3 years,

CI = A – P = ₹ 70,304 – ₹ 62,500 = ₹ 7,804

Hence, amount = ₹ 70304 and CI = ₹ 7804

(d) Given: P = ₹ 8,000, n = 1 years R = 9% per annum compounded half yearly

Since, the interest is compounded half yearly n = 1 × 2 = 2 half years

CI = A – P = ₹ 8,736.20 – ₹ 8,000 = ₹ 736.20

Hence, the amount = ₹ 8736.20 and CI = ₹ 736.20

(e) Given: P = ₹ 10,000, n = 1 year and R = 8% pa compounded half yearly

Since the interest is compounded half yearly n = 1 × 2 = 2 half years

CI = A – P = ₹ 10,816 – ₹ 10,000 = ₹ 816

Hence the amount = ₹ 10,816 and Cl = ₹ 816

Question 2.

Kamala borrowed ₹ 26,400 from a Bank to buy a scooter at a rate of 15% per annum compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find amount for 2 years with interest is compounded yearly and then find SI on the 2nd

Solution:

Given:

P = ₹ 26,400

R = 15% p.a. compounded yearly

n = 2 years and 4 months

Amount after 2 years and 4 months = ₹ 34,914 + ₹ 1745.70 = ₹ 36,659.70

Hence, the amount to be paid by Kamla = ₹ 36,659.70

Question 3.

Fabina borrows ₹ 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?

Solution:

For Fabina: P = ₹ 12,500, R = 12% p.a. and n = 3 years

Difference between the two interests = ₹ 4500 – ₹ 4137.50 = ₹ 362.50

Hence, Fabina pays more interest by ₹ 362.50.

Question 4.

I borrowed ₹ 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?

Solution:

Given: P = ₹ 12,000, R = 6% p.a., n = 2 years

Difference between two interests = ₹ 1483.20 – ₹ 1440 = ₹ 43.20

Hence, the extra amount to be paid = ₹ 43.20

Question 5.

Vasudevan invested ₹ 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get

(i) after 6 months?

(ii) after 1 year?

Solution:

(i) Given: P = ₹ 60,000, R = 12% p.a. compounded half yearly

Hence, the required amount = ₹ 67416

Difference between the amounts = ₹ 92,610 – ₹ 92,400 = ₹ 210

Question 7.

Maria invested ₹ 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find

(i) The amount credited against her name at the end of the second year.

(ii) The interest for the third year.

Solution:

(i) Given: P = ₹ 8,000, R = 5% p.a.

and n = 2 years

Hence, interest for the third year = ₹ 441

Total interest = ₹ 1,000 + ₹ 550 = ₹ 1,550

Difference between the two interests = ₹ 1,576.25 – ₹ 1,550 = ₹ 26.25

Hence, the interest will be ₹ 26.25 more when compounded half yearly than the interest when compounded annually.

Hence, the required amount = ₹ 4913

Question 10.

The population of a place increased to 54,000 in 2003 at a rate of 5% per annum.

(i) Find the population in 2001.

(ii) What would be its population in 2005?

Solution:

(i) Given: Population in 2003 = 54,000

Rate = 5% pa

Time = 2003 – 2001 = 2 years

Population in 2003 = Population in 2001

Question 11.

In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.

Solution:

Given: Initial count of bacteria = 5,06,000

Rate = 2.5% per hour

n = 2 hours

Number of bacteria at the end of 2 hours = Number of count of bacteria initially

Thus, the number of bacteria after two hours = 5,31,616 (approx).

Question 12.

A scooter was bought at ₹ 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.

Solution:

Given: Cost price of the scooter = ₹ 42,000

Rate of depreciation = 8% p.a.

Time = 1 year

Final value of the scooter

Hence, the value of scooter after 1 year = ₹ 38,640.