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Samacheer Kalvi 7th Maths (Term 3) Percentage and Simple Interest Exercise Solutions

Complete TN Class 7 Maths (Term 3) Percentage and Simple Interest exercise solutions with step-by-step workings, all exercise answers, and exam tips.

Updated 12 June 202621 min read

Exercise Solutions Available

Step-by-step answers for all textbook questions in this chapter

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How to Use This Page

Use this page alongside your Samacheer Kalvi textbook. Attempt each exercise on your own first, then compare your method and answer with the step-by-step solutions below. Pay special attention to the working steps — exams award marks for method, not just final answers.

Key Concepts (Quick Recap)

  • Percentage means "per hundred." The symbol % equals 1/100.
  • Fraction to percentage: Multiply by 100. Example: 3/4 × 100 = 75%
  • Percentage to fraction: Remove % sign, divide by 100, simplify. Example: 65% = 65/100 = 13/20
  • Decimal to percentage: Multiply by 100 and add %. Example: 0.282 × 100 = 28.2%
  • Percentage to decimal: Divide by 100 (shift decimal two places left). Example: 21% = 0.21
  • Finding a percentage of a quantity: (Percentage / 100) × Quantity. Example: 25% of 7500 = (25/100) × 7500 = 1875
  • Simple Interest formula: I = Pnr / 100 where P = Principal, n = Time in years, r = Rate % per annum
  • Amount formula: A = P + I
  • Finding P: P = (I × 100) / (n × r)
  • Finding r: r = (I × 100) / (P × n)
  • Finding n: n = (I × 100) / (P × r)
  • Time in months: Convert to years by dividing by 12. Example: 2 years 3 months = 2 + 3/12 = 9/4 years

Exercise 2.1

Question 1

In each of the following grids, find the number of coloured squares and express it as a fraction, decimal and percentage.

(i) Coloured squares = 58, Total = 100

Fraction = 58/100 Decimal = 0.58 Percentage = (58/100) × 100% = 58%

(ii) Coloured squares = 53, Total = 100

Fraction = 53/100 Decimal = 0.53 Percentage = (53/100) × 100% = 53%

(iii) Coloured squares = 25, Total = 50

Fraction = 25/50 Decimal = (25/50) × (2/2) = 50/100 = 0.50 Percentage = (25/50) × 100% = 50%

(iv) Coloured squares = 17, Total = 25

Fraction = 17/25 Decimal = (17/25) × (4/4) = 68/100 = 0.68 Percentage = (17/25) × 100% = 68%

(v) Coloured squares = 15, Total = 30

Fraction = 15/30 Decimal = (1/2) = 0.50 Percentage = (15/30) × 100% = 50%

Question 2

A chess board has 64 squares. Find the percentage of (i) white coloured squares, (ii) grey coloured squares, (iii) squares that have pieces, (iv) squares that do not have pieces.

(i) White squares = 32

Percentage = (32/64) × 100% = 50%

(ii) Grey squares = 32

Percentage = (32/64) × 100% = 50%

(iii) Squares with pieces = 20

Percentage = (20/64) × 100% = 31.25%

(iv) Squares without pieces = 44

Percentage = (44/64) × 100% = 68.75%

Question 3

A dart board has 20 sectors. Find the percentage of white and black portions. (White = 10, Black = 10)

White percentage = (10/20) × 100% = 50% Black percentage = (10/20) × 100% = 50%

Question 4

Write each fraction as a percentage.

(i) 36/50

(36/50) × 100% = 72%

(ii) 81/30

(81/30) × 100% = 270%

(iii) 42/56

42/56 = 21/28 = 3/4 (3/4) × 100% = 75%

(iv) 2 and 1/4 = 9/4

(9/4) × 100% = 225%

(v) 1 and 3/5 = 8/5

(8/5) × 100% = 160%

Question 5

Anbu scored 436 marks out of 500. What was the percentage?

Given: Scored = 436, Total = 500 Formula: Percentage = (Scored / Total) × 100 = (436/500) × 100% = 87.2%
Answer87.2%

Question 6

Write each percentage as a fraction.

(i) 21% = 21/100

(ii) 93.1%

93.1/100 = (93.1 × 10)/(100 × 10) = 931/1000

(iii) 151% = 151/100

(iv) 65%

65/100 = 13/20

(v) 0.64%

0.64/100 = (0.64 × 100)/(100 × 100) = 64/10000 = 4/625

Question 7

Iniyan bought 5 dozen eggs. Out of that, 10 are rotten. Express the good eggs as a percentage.

Given: 5 dozen = 5 × 12 = 60 eggs total Rotten = 10, Good = 60 - 10 = 50 Percentage of good eggs = (50/60) × 100% = (5/6) × 100% = 83.33%
Answer83.33%

Question 8

In an election, Candidate X secured 48% of votes. What fraction represents his votes?

48% = 48/100 = 12/25
Answer12/25

Question 9

Ranjith's total income was Rs 7,500. He saved 25%. Find the amount saved.

Given: Income = Rs 7,500, Savings = 25% Amount saved = (25/100) × 7500 = Rs 1,875
AnswerRs 1,875

Objective Type Questions

Q1: Thendral saved one fourth of her salary. Her savings percentage is:

  • (i) 3/4 (ii) 1/4% (iii) 25% (iv) 1%
1/4 × 100% = 25%
Answer(iii) 25%

Q2: Kavin scored 15 out of 25 in a test. The percentage is:

  • (i) 60% (ii) 15% (iii) 25% (iv) 15/25
(15/25) × 100% = 60%
Answer(i) 60%

Q3: 0.07% is:

  • (i) 7/10 (ii) 7/100 (iii) 7/1000 (iv) 7/10000
0.07% = 0.07/100 = 7/10000
Answer(iv) 7/10000

Exercise 2.2

Question 1

Write each percentage as a decimal.

(i) 21%

21% = 21/100 = 0.21

(ii) 93.1%

93.1% = 93.1/100 = 0.931

(iii) 151%

151% = 151/100 = 1.51

(iv) 65%

65% = 65/100 = 0.65

(v) 0.64%

0.64% = 0.64/100 = 0.0064

Question 2

Convert each decimal as a percentage.

(i) 0.282

0.282 × 100% = 28.2%

(ii) 1.51

1.51 × 100% = 151%

(iii) 1.09

1.09 × 100% = 109%

(iv) 0.71

0.71 × 100% = 71%

(v) 0.858

0.858 × 100% = 85.8%

Question 3

A student scored 75% of marks. Express as a decimal.

75% = 75/100 = 0.75

Question 4

In a village 70.5% people are literate. Express as a decimal.

70.5% = 70.5/100 = 0.705

Question 5

Scoring rate of a batsman is 86%. Write as decimal.

86% = 86/100 = 0.86

Question 6

The height of a flag pole is 6.75 m. Express it as a percentage.

6.75 = 675/100 = 6.75 × 100% = 675%

Question 7

The weights of two chemical substances are 20.34 g and 18.78 g. Write the difference in percentage.

Difference = 20.34 - 18.78 = 1.56 Percentage difference = (1.56/18.78) × 100% ≈ 8.30%

Question 8

Find the percentage of the shaded region. (1 shaded out of 4 parts)

Fraction shaded = 1/4 Percentage = (1/4) × 100% = 25%

Objective Type Questions

Q1: Decimal value of 142.5% is:

142.5% = 142.5/100 = 1.425
Answer(i) 1.425

Q2: The percentage of 0.005 is:

0.005 × 100% = 0.5%
Answer(iii) 0.5%

Q3: The percentage of 4.7 is:

4.7 × 100% = 470%
Answer(iv) 470%

Exercise 2.3

Question 1

Out of 70 magazines at a bookstore, 14 are comedy magazines. What percentage are comedy?

Given: Total = 70, Comedy = 14 Percentage = (14/70) × 100% = (1/5) × 100% = 20%
Answer20%

Question 2

A tank holds 50 litres of water. It is 30% full. How many litres are needed to fill it to 50%?

Given: Capacity = 50 L, Current = 30% full Current water = (30/100) × 50 = 15 L Water at 50% = (50/100) × 50 = 25 L Water needed = 25 - 15 = 10 L
Answer10 litres

Question 3

Karun bought shoes at 25% discount and paid Rs 1,000. Find the marked price.

Given: Discount = 25%, Amount paid = Rs 1,000 Let marked price = P P - (25% of P) = 1000 P - (1/4)P = 1000 (3/4)P = 1000 P = 1000 × (4/3) = Rs 1,333.33
AnswerRs 1,333.33 (approx)

Question 4

An insurance agent earns 5% commission on Rs 4,800 collected. Find the commission.

Given: Collection = Rs 4,800, Commission rate = 5% Commission = (5/100) × 4800 = Rs 240
AnswerRs 240

Question 5

A biology class examined 40 flowers. 30 were perennials. What percentage were perennials?

Given: Total = 40, Perennials = 30 Percentage = (30/40) × 100% = 75%
Answer75%

Question 6

Ismail ordered 50 beads, of which 15 were brown. Find the percentage of brown beads.

Given: Total = 50, Brown = 15 Percentage = (15/50) × 100% = 30%
Answer30%

Question 7

Ramu scored 20/25 in English, 30/40 in Science, and 68/80 in Mathematics. Which is best?

English percentage = (20/25) × 100% = 80% Science percentage = (30/40) × 100% = 75% Mathematics percentage = (68/80) × 100% = 85% Best: Mathematics at 85%
AnswerMathematics (85%)

Question 8

Peter needs 50% to pass. He scored 280 marks and fell short by 20 marks. Find maximum marks.

Given: Score = 280, Short by = 20 Passing marks = 280 + 20 = 300 50% of total = 300 Total = 300 × 2 = 600
AnswerMaximum marks = 600

Question 9

Kayal scored 225/500 in test 1 and 265/500 in test 2. Find the percentage increase.

Given: Test 1 = 225, Test 2 = 265, Total = 500 Change = 265 - 225 = 40 Percentage increase = (40/500) × 100% = 8%
Answer8% increase

Question 10

Roja earns Rs 18,000/month and uses her salary in ratio 2:1:3 for education, savings, and other expenses. Express as percentages.

Total parts = 2 + 1 + 3 = 6 Education: (2/6) × 18000 = Rs 6,000 → (6000/18000) × 100 = 33.33% Savings: (1/6) × 18000 = Rs 3,000 → (3000/18000) × 100 = 16.67% Other expenses: (3/6) × 18000 = Rs 9,000 → (9000/18000) × 100 = 50%
AnswerEducation 33.33%, Savings 16.67%, Other expenses 50%

Exercise 2.4

Question 1

Find the simple interest on Rs 35,000 at 9% per annum for 2 years.

Given: P = Rs 35,000, r = 9%, n = 2 years Formula: I = Pnr/100 Substitution: I = (35000 × 2 × 9) / 100 I = 630000 / 100 I = Rs 6,300
AnswerSimple Interest = Rs 6,300

Question 2

Aravind borrowed Rs 8,000 at 7% per annum. Find interest and amount after 2 years.

Given: P = Rs 8,000, r = 7%, n = 2 years Formula: I = Pnr/100 Substitution: I = (8000 × 2 × 7) / 100 I = 112000 / 100 I = Rs 1,120 Amount = P + I = 8000 + 1120 = Rs 9,120
AnswerInterest = Rs 1,120, Amount = Rs 9,120

Question 3

Sheela paid simple interest of Rs 21,280 for 4 years at 9.5% per annum. Find the sum (principal).

Given: I = Rs 21,280, r = 9.5%, n = 4 years Formula: I = Pnr/100 Substitution: 21280 = (P × 4 × 9.5) / 100 21280 = 38P / 100 P = (21280 × 100) / 38 P = 2128000 / 38 P = Rs 56,000
AnswerPrincipal = Rs 56,000

Question 4

Basha borrowed Rs 8,500 at a certain rate. After 3 years, he paid Rs 11,050. Find the rate of interest.

Given: P = Rs 8,500, n = 3 years, A = Rs 11,050 Step 1 — Find Interest: I = A - P = 11050 - 8500 = Rs 2,550 Step 2 — Find Rate: r = (I × 100) / (P × n) r = (2550 × 100) / (8500 × 3) r = 255000 / 25500 r = 10%
AnswerRate = 10% per annum

Question 5

In what time will Rs 16,500 amount to Rs 22,935 at 13% per annum?

Given: P = Rs 16,500, r = 13%, A = Rs 22,935 Step 1 — Find Interest: I = A - P = 22935 - 16500 = Rs 6,435 Step 2 — Find Time: n = (I × 100) / (P × r) n = (6435 × 100) / (16500 × 13) n = 643500 / 214500 n = 3 years
Answer3 years

Question 6

In what time will Rs 17,800 amount to Rs 19,936 at 6% per annum?

Given: P = Rs 17,800, r = 6%, A = Rs 19,936 Step 1 — Find Interest: I = A - P = 19936 - 17800 = Rs 2,136 Step 2 — Find Time: n = (I × 100) / (P × r) n = (2136 × 100) / (17800 × 6) n = 213600 / 106800 n = 2 years
Answer2 years

Question 7

A sum of Rs 48,000 was lent out at simple interest. After 2 years 3 months, the total amount was Rs 55,560. Find the rate per year.

Given: P = Rs 48,000, A = Rs 55,560 n = 2 years 3 months = 2 + 3/12 = 9/4 years Step 1 — Find Interest: I = A - P = 55560 - 48000 = Rs 7,560 Step 2 — Find Rate: r = (I × 100) / (P × n) r = (7560 × 100) / (48000 × 9/4) r = 756000 / 108000 r = 7%
AnswerRate = 7% per annum

Question 8

A principal becomes Rs 17,000 at 12% in 3 years. Find the principal.

Given: A = Rs 17,000, r = 12%, n = 3 years We know: A = P + I and I = Pnr/100 So: A = P + (P × 3 × 12)/100 A = P + 36P/100 A = P(1 + 36/100) A = P × 136/100 17000 = P × 136/100 P = (17000 × 100) / 136 P = 1700000 / 136 P = Rs 12,500
AnswerPrincipal = Rs 12,500

Objective Type Questions

Q9: Interest for a principal of Rs 4,500 which gives an amount of Rs 5,000:

I = A - P = 5000 - 4500 = Rs 500
Answer(i) Rs 500

Q10: Simple interest for Rs 1,000 for 1 year at 10%:

I = (1000 × 1 × 10)/100 = Rs 100
Answer(iii) Rs 100

Q11: Rate yielding Rs 200 interest on Rs 2,000 for 1 year:

r = (200 × 100)/(2000 × 1) = 10%
Answer(i) 10%

Exercise 2.5

Miscellaneous Practice Problems

Q1

Mathi put down a deposit of 1/10 of the flat's value. What percentage was this?

1/10 × 100% = 10%
Answer10%

Q2

Yazhini scored 15 out of 25. Express as percentage.

(15/25) × 100% = 60%
Answer60%

Q3

Out of 120 teachers, 70 were male. Express male teachers as percentage.

(70/120) × 100% = 700/12 = 58.33%
Answer58.33%

Q4

A cricket team won 70 matches, lost 28, no result for 2. Find percentage of matches won.

Total matches = 70 + 28 + 2 = 100 Percentage won = (70/100) × 100% = 70%
Answer70%

Q5

500 students in a school; 370 can swim. What percentage can swim and cannot swim?

Can swim: (370/500) × 100% = 74% Cannot swim: 500 - 370 = 130 Cannot swim: (130/500) × 100% = 26%
Answer74% can swim, 26% cannot swim

Q6

Ratio of Saral's income to savings is 4:1. Percentage of money saved?

Total parts = 4 + 1 = 5 Savings = 1 part Percentage saved = (1/5) × 100% = 20%
Answer20%

Q7

A salesman earns 5% commission on sales worth Rs 1,500. Find the commission.

Commission = (5/100) × 1500 = Rs 75
AnswerRs 75

Q8

A World Cup ticket was Rs 1,500. Price increased by 18%. Find new price.

Increase = (18/100) × 1500 = Rs 270 New price = 1500 + 270 = Rs 1,770
AnswerRs 1,770

Q9

2 is what percentage of 50?

x% of 50 = 2 (x/100) × 50 = 2 x = (2 × 100)/50 = 4%
Answer4%

Q10

What percentage of 8 is 64?

x% of 8 = 64 (x/100) × 8 = 64 x = (64 × 100)/8 = 800%
Answer800%

Q11

Stephen invested Rs 10,000 at 2% simple interest for 4 years. Find the interest.

Given: P = Rs 10,000, r = 2%, n = 4 years I = Pnr/100 = (10000 × 4 × 2)/100 = Rs 800
AnswerInterest = Rs 800

Q12

Riya borrowed Rs 15,000 at 10% SI and paid Rs 9,000 as interest. Find the time.

Given: P = Rs 15,000, r = 10%, I = Rs 9,000 I = Pnr/100 9000 = (15000 × n × 10)/100 n = (9000 × 100)/(15000 × 10) = 6 years
Answer6 years

Q13

In what time will SI on Rs 3,000 at 8% equal SI on Rs 4,000 at 12% for 4 years?

Step 1 — Find interest on second investment: I₂ = (4000 × 12 × 4)/100 = Rs 1,920 Step 2 — Set up equation for first investment: I₁ = (3000 × 8 × n)/100 = 240n Step 3 — Equate: 240n = 1920 n = 1920/240 = 8 years
Answer8 years

Challenge Problems

Q14

A man travelled 80 km by car and 320 km by train. Find percentage by car and by train.

Total distance = 80 + 320 = 400 km By car: (80/400) × 100% = 20% By train: (320/400) × 100% = 80%
AnswerCar 20%, Train 80%

Q15

Lalitha got 35 correct and 10 incorrect answers. Percentage of correct answers?

Total answers = 35 + 10 = 45 Percentage correct = (35/45) × 100% = 77.78%
Answer77.78%

Q17

Population of a village is 8,000. 80% are literate, and of those, 40% are women. Find percentage of literate women to total population.

Literate people = 80% of 8000 = (80/100) × 8000 = 6400 Literate women = 40% of 6400 = (40/100) × 6400 = 2560 Percentage of literate women to total = (2560/8000) × 100% = 32%
Answer32%

Q18

A student earned 80% on a 20-problem test. How many did he answer correctly?

Correct answers = (80/100) × 20 = 16
Answer16 problems

Q19

A metal bar weighs 8.5 kg. 85% is silver. How many kg of silver?

Silver weight = (85/100) × 8.5 = 7.225 kg
Answer7.225 kg

Q20

Concession card holders pay Rs 120 for a train ticket. Full fare is Rs 230. Find percentage discount.

Discount = 230 - 120 = Rs 110 Percentage discount = (110/230) × 100% = 47.83%
Answer47.83%

Q21

A tank holds 200 L, currently 40% full. How many litres to fill to 75%?

Current water = (40/100) × 200 = 80 L Target water = (75/100) × 200 = 150 L Water needed = 150 - 80 = 70 L
Answer70 litres

Q22

Which is greater: 16 and 2/3%, 2/5, or 0.17?

Convert all to percentage: 16 2/3% = 16.67% 2/5 = (2/5) × 100% = 40% 0.17 = 17/100 = 17% Comparing: 40% > 17% > 16.67% Greatest: 2/5 (40%)
Answer2/5 (40%) is the greatest

Q23

A machine depreciates at 10% per year. Present value Rs 1,62,000. Find worth after 2 years.

Year 1: Depreciation = (10/100) × 1,62,000 = Rs 16,200 Worth after year 1 = 1,62,000 - 16,200 = Rs 1,45,800 Year 2: Depreciation = (10/100) × 1,45,800 = Rs 14,580 Worth after year 2 = 1,45,800 - 14,580 = Rs 1,31,220
AnswerRs 1,31,220

Q24

A sum amounts to Rs 6,200 in 2 years and Rs 6,800 in 3 years. Find principal and rate.

Step 1 — Find interest for 1 year: Interest for 1 year = 6800 - 6200 = Rs 600 Step 2 — Find principal: Interest for 2 years = 2 × 600 = Rs 1,200 P = A - I = 6200 - 1200 = Rs 5,000 Step 3 — Find rate: r = (I × 100)/(P × n) r = (600 × 100)/(5000 × 1) = 12%
AnswerPrincipal = Rs 5,000, Rate = 12% per annum

Q25

Rs 46,900 was lent at SI. After 2 years, total amount was Rs 53,466. Find the rate.

Given: P = Rs 46,900, n = 2, A = Rs 53,466 Interest = 53466 - 46900 = Rs 6,566 r = (I × 100)/(P × n) r = (6566 × 100)/(46900 × 2) r = 656600/93800 = 7%
Answer7% per annum

Q26

Arun lent Rs 5,000 to Balaji for 2 years and Rs 3,000 to Charles for 4 years at the same rate. Total interest received = Rs 2,200. Find the rate.

Interest from Balaji = (5000 × 2 × r)/100 = 100r Interest from Charles = (3000 × 4 × r)/100 = 120r Total interest: 100r + 120r = 2200 220r = 2200 r = 10%
Answer10% per annum

Q27

If a principal doubles in 4 years, find the rate of interest.

Let P = Rs 100 Amount after 4 years = Rs 200 (doubled) Interest = 200 - 100 = Rs 100 I = Pnr/100 100 = (100 × 4 × r)/100 4r = 100 r = 25%
Answer25% per annum

Common Mistakes

1. Forgetting to divide by 100 in SI formula: Students write I = P × r × n instead of I = (P × r × n) / 100. Always divide by 100.

2. Not converting months to years: When time is given as "2 years 3 months," you must convert: 2 + 3/12 = 9/4 years. Using 2.3 years directly is wrong.

3. Confusing "percentage of" with "percentage increase/decrease": "What % is 15 of 25?" uses (part/whole) × 100. "What is the % increase from 200 to 260?" uses (increase/original) × 100.

4. Mixing up Amount and Principal: Amount A = Principal + Interest (A = P + I). Students sometimes substitute A in place of P or vice versa in the SI formula.

5. Errors in fraction-to-percentage conversion: Always multiply by 100. For mixed fractions like 2 and 1/4, first convert to an improper fraction (9/4) before multiplying by 100.

6. Forgetting to find Interest first in rate/time problems: When given P and A, first compute I = A - P, then use I in the formula to find r or n.

7. Depreciation is on the reduced value, not the original: In successive depreciation, each year's 10% is on the new (reduced) value, not the original price.

Exam Checklist

  • [ ] Can convert between fractions, decimals, and percentages fluently
  • [ ] Can find a percentage of a given quantity (e.g., 25% of 7500)
  • [ ] Can find what percentage one number is of another
  • [ ] Know the SI formula: I = Pnr/100 and all its rearrangements
  • [ ] Can find P when I, r, n are given: P = (I × 100) / (n × r)
  • [ ] Can find r: r = (I × 100) / (P × n)
  • [ ] Can find n: n = (I × 100) / (P × r)
  • [ ] Remember A = P + I (Amount = Principal + Interest)
  • [ ] Convert months to years correctly (divide by 12)
  • [ ] Handle mixed time periods (e.g., 2 years 3 months = 9/4 years)
  • [ ] Percentage increase = (increase / original) × 100
  • [ ] Percentage decrease = (decrease / original) × 100
  • [ ] Depreciation uses the reduced balance, not the original

Frequently Asked Questions

Simple Interest (SI) = (P × R × T) / 100, where P = Principal, R = Rate of interest per annum, and T = Time in years. The total amount A = P + SI.