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.