# DAV Class 8 Maths Chapter 6 Worksheet 2 Solutions

The DAV Class 8 Maths Book Solutions Pdf and DAV Class 8 Maths Chapter 6 Worksheet 2 Solutions of Profit, Loss and Discount offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 6 WS 2 Solutions

Question 1.
Compute the compound interest on ₹ 5000 for 1$$\frac{1}{2}$$ years at 16% p.a. compounded half-yearly.
Solution:
Here P = ₹ 5000,
R = $$\frac{16}{2}$$ %
= 8% per half year

and T = 1$$\frac{1}{2}$$ years
= $$\frac{3}{2}$$ years
= $$\frac{1}{2}$$ × 2 = 3 half years

Interest for the first half year = $$\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}$$
= $$\frac{5000 \times 8 \times 1}{100}$$
= ₹ 400

Principal for the second half year = ₹ 5000 + ₹ 400
= ₹ 5400

Interest for the second half year = $$\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}$$
= $$\frac{5400 \times 8 \times 1}{100}$$
= ₹ 432

Principal for the third half year = ₹ 5400 + ₹ 432
= ₹ 5832

Interest for the third half year = $$\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}$$
= $$\frac{5832 \times 8 \times 1}{100}$$
= ₹ 466.56

∴ Amount at the end of third half year = ₹ 5832 + ₹ 466.56
= ₹ 6298.56

C.I. = A – P
= ₹ 6298.56 – ₹ 5000
= ₹ 1298.56

Hence, the required compound interest is ₹ 1298.56.

Question 2.
Find the compound interest on ₹ 15625 at 16% p.a. for 9 months when compounded quarterly.
Solution:
Here P = ₹ 15625,
R = $$\frac{16}{4}$$ %
= 4% per quarter
and T = $$\frac{9}{12}$$ × 4 = 3 years

Interest for the first half year = $$\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}$$
= $$\frac{15625 \times 4 \times 1}{100}$$
= ₹ 625

Principal for the second quarter = ₹ 15625 + ₹ 625
= ₹ 16250

Interest for the second quarter = $$\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}$$
= $$\frac{16250\times 4 \times 1}{100}$$
= ₹ 650

Principal for the third quarter = ₹ 16250 + ₹ 650
= ₹ 16900

Interest for the third quarter = $$\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}$$
= $$\frac{16900 \times 4 \times 1}{100}$$
= ₹ 676

Amount at the end of third quarter = ₹ 16900 + ₹ 676
= ₹ 17576

∴ C.I. = A – P
= ₹ 17576 – ₹ 15625
= ₹ 1951

Hence, the compound interest is ₹ 1951.

Question 3.
Rohit deposited ₹ 10,000 in a bank for 6 months. If the bank pays compound interest at 12% p.a., reckoned quarterly, find the amount to be received by him on maturity.
Solution:
Here P = ₹ 10,000,
R = $$\frac{12}{4}$$ %
= 3% quarterly,

T = $$\frac{6}{12}$$ × 4
= 2 quarters.

Interest for the first half year = $$\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}$$
= $$\frac{10000 \times 3 \times 1}{100}$$
= ₹ 300

Principal for the second quarter = ₹ 10000 + ₹ 300
= ₹ 10,300

Interest for the second half year = $$\frac{\mathrm{P} \times \mathrm{R} \times \mathrm{T}}{100}$$
= $$\frac{10300 \times 3 \times 1}{100}$$
= ₹ 309

∴ Amount at the end of second quarter = ₹ 10300 + ₹ 309
= ₹ 10609
Hence, the amount to be received by him at the end of 6 months is ₹ 10609.

Question 4.
Find the difference between the compound interest on ₹ 25000 at 16% p.a. for 6 months compounded half yearly and quarterly respectively. Which option is better?
Solution:
Case I:
When the interest is compounded half yearly,
P = ₹ 25000,
R = $$\frac{16}{2}$$
= 8% per half year
and T = $$\frac{6}{12}$$ × 2
= 1 half year

Interest for the first half year = $$\frac{P \times R \times T}{100}$$
= $$\frac{25000 \times 8 \times 1}{100}$$
= ₹ 2000

Case II:
When the interest is compounded quarterly,
P = ₹ 25000,
R = $$\frac{16}{4}$$
= 4% per quarter
and T = $$\frac{6}{12}$$ × 4
= 2 quarters

Interest for the first quarter = $$\frac{P \times R \times T}{100}$$
= $$\frac{25000 \times 4 \times 1}{100}$$
= ₹ 1000

Principal for the second quarter = ₹ 25000 + ₹ 1000
= ₹ 26000

Interest for the second quarter = $$\frac{P \times R \times T}{100}$$
= $$\frac{26000 \times 4 \times 1}{100}$$
= ₹ 1040

Amount at the end of second quarter = ₹ 26000 + ₹ 1040
= ₹ 27040

∴ C.I. = A – P = ₹ 27040 – ₹ 25000
= ₹ 2040

∴ Difference between the two C.I.s = ₹ 2040 – ₹ 2000
= ₹ 240
Hence, the second option is better.

Question 5.
Bela borrowed ₹ 25000 from a finance company to start her boutique at 20% p.a. compounded half yearly. What amount of money will clear her debt after 1$$\frac{1}{2}$$ years?
Solution:
Here P = ₹ 25000,
R = $$\frac{20}{2}$$
= 10% per half year
T = 1$$\frac{1}{2}$$ years
= $$\frac{3}{2}$$ years
= $$\frac{3}{2}$$ × 2
= 3 half years

Interest for the first half year = $$\frac{P \times R \times T}{100}$$
= $$\frac{25000 \times 10 \times 1}{100}$$
= ₹ 2500

Principal for the second half year = ₹ 25000 + ₹ 2500
= ₹ 27500

Interest for the second half year = $$\frac{P \times R \times T}{100}$$
= $$\frac{27500 \times 10 \times 1}{100}$$
= ₹ 2750

Principal for the third half year = ₹ 27500 + ₹ 2750
= ₹ 30250

Interest for the third half year = $$\frac{P \times R \times T}{100}$$
= $$\frac{30250 \times 10 \times 1}{100}$$
= ₹ 3025

∴ Amount after third half year = ₹ 30250 + ₹ 3025
= ₹ 33275

Hence, the amount = ₹ 17496.