CG Board Class 8 Mathematics Chapter 13 Solutions: Application of Percentage (प्रतिशतता के अनुप्रयोग) – 2026-27

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CG SCERT (Chhattisgarh Board) Class 8 Mathematics Solutions | 2026-27 Official Edition

Complete 100% textbook-grounded CG Board Class 8 Mathematics Chapter 13 Solutions: Application of Percentage (प्रतिशतता के अनुप्रयोग) in Bilingual Format (English & Hindi Medium).

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Question 1

Find the compound interest for


📝 Question:

Find the compound interest for:**

💡 Solution:

(i) Rs. 4000 at the rate of 5% for 2 years.**

Given: Principal P = Rs. 4000, Rate R = 5\% p.a., Time T = 2 years.

A = P (1 + R/100)T = 4000 (1 + 5/100)2 = 4000 (21/20)2 = 4000 × 441/400 = Rs. 4410

Compound Interest (C.I.) = A – P = 4410 – 4000 = Rs. 410

  • (ii) Rs. 6000 at the rate of 10% for 3 years.

Given: P = Rs. 6000, R = 10\%, T = 3 years.

A = 6000 (1 + 10/100)3 = 6000 × (11/10)3 = 6000 × (1331)/(1000) = 6 × 1331 = Rs. 7986

C.I. = A – P = 7986 – 6000 = Rs. 1986

  • (iii) Rs. 6250 at the rate of 8% for 2 years.

Given: P = Rs. 6250, R = 8\%, T = 2 years.

A = 6250 (1 + 8/100)2 = 6250 × (27/25)2 = 6250 × 729/625 = 10 × 729 = Rs. 7290

C.I. = A – P = 7290 – 6250 = Rs. 1040

Question 2

Find the amount while interest is calculated every…


📝 Question:

Find the amount while interest is calculated every year:**

💡 Solution:

(i) Rs. 7500 at the rate of 6% for 2 years.**

A = 7500 (1 + 6/100)2 = 7500 × (53/50)2 = 7500 × (2809)/(2500) = 3 × 2809 = Rs. 8427

  • (ii) Rs. 2500 at the rate of 8% for 2 years.

A = 2500 (1 + 8/100)2 = 2500 × (27/25)2 = 2500 × 729/625 = 4 × 729 = Rs. 2916

  • (iii) Rs. 5120 at the rate of 12 1/2 % for 2 years.

Here R = 12.5\% = 25/2\%.

A = 5120 (1 + 25/200)2 = 5120 × (9/8)2 = 5120 × 81/64 = 80 × 81 = Rs. 6480

Question 3

A farmer wanted to buy a diesel pump…


📝 Question:

A farmer wanted to buy a diesel pump and took a loan of Rs. 5500 from the rural bank at 4% annual compound interest. Calculate annually and find out how much money will the farmer return to the bank after 2 years.**

💡 Solution:

Given: P = Rs. 5500, R = 4\%, T = 2 years.

A = 5500 (1 + 4/100)2 = 5500 × (26/25)2 = 5500 × 676/625 = 8.8 × 676 = Rs. 5948.80

Question 4

Anuradha deposited Rs 8000 in an institute at…


📝 Question:

Anuradha deposited Rs. 8000 in an institute at 5% interest per annum in Compound interest. Find out the amount of money that she would get after a period of 3 years.**

💡 Solution:

Given: P = Rs. 8000, R = 5\%, T = 3 years.

A = 8000 (1 + 5/100)3 = 8000 × (21/20)3 = 8000 × (9261)/(8000) = Rs. 9261

Question 1

In a savings bank account the bank offers…


📝 Question:

In a savings bank account the bank offers an annual compound interest of 5%. If the interest is added to the principal amount every 6 months, then how much interest will Naresh get after 1 year if he deposited Rs. 1600 in the bank?**

💡 Solution:

Given: P = Rs. 1600, Annual Rate = 5%, Time = 1 year.

Since interest is compounded half yearly (every 6 months)

Half-yearly rate R = 5/2\% = 2.5\%, Number of half-years n = 2.

A = 1600 (1 + 2.5/100)2 = 1600 × (41/40)2 = 1600 × (1681)/(1600) = Rs. 1681

Interest = A – P = 1681 – 1600 = Rs. 81

Question 2

Anamika deposited Rs 24000 at 10 annual interest…


📝 Question:

Anamika deposited Rs. 24000 at 10% annual interest for 1 1/2 years. If the interest is calculated every 6 months, how much money will she get on maturity?**

💡 Solution:

Given: P = Rs. 24000, Annual Rate = 10%, Time = 11/2 years.

Half-yearly rate R = 10/2\% = 5\%, Number of conversion periods n = 3 half-years.

A = 24000 (1 + 5/100)3 = 24000 × (21/20)3 = 24000 × (9261)/(8000) = 3 × 9261 = Rs. 27783

Question 3

Find out the difference between the compound interest…


📝 Question:

Find out the difference between the compound interest and simple interest for Rs. 7500 at the rate of 8% per annum for one year. Note that Compound interest is calculated every 6 months.**

💡 Solution:

Given: P = Rs. 7500, R = 8\%, T = 1 year.

  1. Simple Interest (S.I.):

S.I. = (P × R × T)/(100) = (7500 × 8 × 1)/(100) = Rs. 600

  1. Compound Interest (C.I. half-yearly):

Half-yearly rate R = 4\%, n = 2 half-years.

A = 7500 (1 + 4/100)2 = 7500 × (26/25)2 = 7500 × 676/625 = 12 × 676 = Rs. 8112

C.I. = 8112 – 7500 = Rs. 612

  1. Difference: 612 – 600 = Rs. 12.

Question 4

What will be the compound interest on a…


📝 Question:

What will be the compound interest on a principal of Rs. 8000 in 1 year when rate of interest is 5% per annum. Note that interest is calculated every 6 months.**

💡 Solution:

Given: P = Rs. 8000, Annual Rate = 5%, Time = 1 year.

Half-yearly rate R = 2.5\%, n = 2 half-years.

A = 8000 (1 + 2.5/100)2 = 8000 × (41/40)2 = 8000 × (1681)/(1600) = 5 × 1681 = Rs. 8405

C.I. = A – P = 8405 – 8000 = Rs. 405

Question 1

Find out the compound interest and amount for…


📝 Question:

Find out the compound interest and amount for the following:**

💡 Solution:

(i) Principal = Rs. 6000, Time = 3 years, Rate = 10% annual**

A = 6000 (1 + 10/100)3 = 6000 × (1331)/(1000) = Rs. 7986

C.I. = 7986 – 6000 = Rs. 1986

  • (ii) Principal = Rs. 1600, Time = 2 years, Rate = 5% annual

A = 1600 (1 + 5/100)2 = 1600 × 441/400 = Rs. 1764

C.I. = 1764 – 1600 = Rs. 164

  • (iii) Principal = Rs. 8500, Time = 2 years, Rate = 15% annual

A = 8500 (1 + 15/100)2 = 8500 × 529/400 = Rs. 11241.25

C.I. = 11241.25 – 8500 = Rs. 2741.25

  • (iv) Principal = Rs. 20000, Time = 3 years, Rate = 5% annual

A = 20000 (1 + 5/100)3 = 20000 × (9261)/(8000) = Rs. 23152.50

C.I. = 23152.50 – 20000 = Rs. 3152.50

Question 2

Salma took a loan of Rs 625 from…


📝 Question:

Salma took a loan of Rs. 625 from the Mahila Samiti to purchase a sewing machine. If the rate of interest be 8% calculated annually, then how much money would Salma return to the samiti after 2 years.**

💡 Solution:

Given: P = Rs. 625, R = 8\%, T = 2 years.

A = 625 (1 + 8/100)2 = 625 × (27/25)2 = 625 × 729/625 = Rs. 729

Question 3

Find out the principal that becomes Rs 5832…


📝 Question:

Find out the principal that becomes Rs. 5832 in two years at the rate of 8% compound interest.**

💡 Solution:

Given: A = Rs. 5832, R = 8\%, T = 2 years.

5832 = P (1 + 8/100)2 ⇒ 5832 = P × 729/625

P = (5832 × 625)/(729) = 8 × 625 = Rs. 5000

Question 4

At what percentage of annual interest does Rs…


📝 Question:

At what percentage of annual interest does Rs. 4000 become Rs. 5290 in 2 years if interest be calculated annually.**

💡 Solution:

Given: P = 4000, A = 5290, T = 2 years.

5290 = 4000 (1 + R/100)2 ⇒ (1 + R/100)2 = (5290)/(4000) = 529/400

Taking square root on both sides

1 + R/100 = 23/20 ⇒ R/100 = 23/20 – 1 = 3/20 ⇒ R = 15\%

Question 5

At what rate does the compound interest for…


📝 Question:

At what rate does the compound interest for Rs. 1800 be Rs. 378 in 2 years if interest has been calculated annually.**

💡 Solution:

Given: P = 1800, C.I. = 378, T = 2.

Amount A = P + C.I. = 1800 + 378 = 2178.

2178 = 1800 (1 + R/100)2 ⇒ (1 + R/100)2 = (2178)/(1800) = 121/100

1 + R/100 = 11/10 ⇒ R/100 = 1/10 ⇒ R = 10\%

Question 6

Find out the difference between the simple interest…


📝 Question:

Find out the difference between the simple interest and compound interest for Rs. 3200 at the rate of 12% annually in 2 years.**

💡 Solution:

Given: P = Rs. 3200, R = 12\%, T = 2 years.

  1. S.I. = (3200 × 12 × 2)/(100) = Rs. 768.
  2. A = 3200 (1 + 12/100)2 = 3200 × (28/25)2 = 3200 × 784/625 = 5.12 × 784 = Rs. 4014.08.

C.I. = 4014.08 – 3200 = Rs. 814.08.

  1. Difference = 814.08 – 768 = Rs. 46.08.

Question 1

Sarjues bought a bicycle that costs Rs 1750…


📝 Question:

Sarjues bought a bicycle that costs Rs. 1750. If the rate of sales tax on the cycle is 4%, how much amount have Sarjues paid for the cycle?**

💡 Solution:

Cost of bicycle = Rs. 1750, Sales Tax = 4%.

Sales Tax = (1750 × 4)/(100) = Rs. 70

Total Amount Paid = 1750 + 70 = Rs. 1820

Question 2

The Gram Panchayat Gidhpuri near Mahanadi collects tax…


📝 Question:

The Gram Panchayat Gidhpuri near Mahanadi collects tax of Rs. 20 per cubic metre for the sand from the river bank. If a truck contains 5 cubic metre of sand, then how much tax would the Panchayat collect for 12 such trucks?**

💡 Solution:

Sand in 12 trucks = 12 × 5 = 60 cubic metres.

Tax per cubic metre = Rs. 20.

Total Tax = 60 × 20 = Rs. 1200

Question 3

Anjali bought scents that cost Rs 500 and…


📝 Question:

Anjali bought scents that cost Rs. 500 and ornaments that cost Rs. 800 from a shop. The sale tax on scent is 16% and that on ornaments is 8%. How much amount did Anjali in total pay to the shopkeeper?**

💡 Solution:

  1. Scent: Cost = Rs. 500, Tax = 16\% of 500 = Rs. 80. Amount = Rs. 580.
  2. Ornaments: Cost = Rs. 800, Tax = 8\% of 800 = Rs. 64. Amount = Rs. 864.

Total Amount Paid = 580 + 864 = Rs. 1444

Question 4

A farmer pays Rs 4 per acre as…


📝 Question:

A farmer pays Rs. 4 per acre as land revenue to the government. If Ramdeen has 85 acres of agricultural land, how much land revenue would he pay to the government?**

💡 Solution:

Land area = 85 acres, Rate = Rs. 4 per acre.

Total Land Revenue = 85 × 4 = Rs. 340

Question 5

Municipal Corporation of Sunderpur decided Rs 8 per…


📝 Question:

Municipal Corporation of Sunderpur decided Rs. 8 per square feet as development tax. If the land owned by Bhanuprakash measures 50 feet x 30 feet, how much development tax will he pay?**

💡 Solution:

Area of plot = 50 × 30 = 1500 sq ft. Tax rate = Rs. 8 per sq ft.

Total Development Tax = 1500 × 8 = Rs. 12000

Question 6

Dinesh brings trucks of grains from other states…


📝 Question:

Dinesh brings trucks of grains from other states for Rs. 37500. If 2.5% entry tax is payable on grains, how much entry tax would Dinesh pay?**

💡 Solution:

Grain Value = Rs. 37500, Entry Tax Rate = 2.5%.

Entry Tax Amount = (37500 × 2.5)/(100) = 375 × 2.5 = Rs. 937.50

Question 7

Gram Panchayat Adrena charges house tax of Rs…


📝 Question:

Gram Panchayat Adrena charges house tax of Rs. 25 per house and if there are 216 houses under the Panchayat area, how much income will the village Panchayat have through house tax?**

💡 Solution:

Number of houses = 216, Tax per house = Rs. 25.

Total Income = 216 × 25 = Rs. 5400

Question 8

The Indian government charges 11 production tax on…


📝 Question:

The Indian government charges 11% production tax on tractor over the invested amount. If a tractor produced in a factory costs Rs. 120000, find out the production tax amount for per tractor.**

💡 Solution:

Cost of tractor = Rs. 120000, Production Tax Rate = 11%.

Production Tax Amount = (120000 × 11)/(100) = 1200 × 11 = Rs. 13200

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