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.