.omtex-content-wrapper h1, .omtex-content-wrapper h2, .omtex-content-wrapper h3 { color: #1a5276; } .main-title-box { background: linear-gradient(135deg, #1a5276 0%, #2980b9 100%); color: white; padding: 30px; border-radius: 12px; text-align: center; margin-bottom: 30px; box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1); } .main-title-box h1 { color: white; margin: 0; font-size: 28px; } .exercise-info { font-weight: 600; margin-top: 10px; display: block; text-transform: uppercase; letter-spacing: 1px; } .section-card { background: #fff; border: 1px solid #e1e8ed; border-radius: 10px; padding: 25px; margin-bottom: 25px; box-shadow: 0 2px 8px rgba(0, 0, 0, 0.05); transition: transform 0.2s; } .section-card:hover { border-color: #3498db; } .question-text { font-size: 18px; font-weight: 700; margin-bottom: 15px; display: block; color: #2e4053; } .solution-box { background-color: #f4f9fd; border-left: 5px solid #3498db; padding: 15px 20px; margin-top: 15px; border-radius: 0 8px 8px 0; } .solution-title { font-weight: bold; color: #2874a6; display: block; margin-bottom: 8px; text-transform: uppercase; font-size: 14px; } .fill-blank-answer { color: #7d3c98; font-weight: bold; text-decoration: underline; } .true-false-tag { font-weight: 800; padding: 2px 8px; border-radius: 4px; } .tag-true { color: #27ae60; background: #eafaf1; } .tag-false { color: #c0392b; background: #fdedec; } .objective-options { display: flex; flex-direction: column; gap: 10px; margin: 15px 0; } .option-item { padding: 10px 15px; border: 1px solid #d5dbdb; border-radius: 6px; background: #fdfefe; } .correct-answer { background-color: #d4edda !important; border-color: #c3e6cb !important; color: #155724 !important; font-weight: bold; } .math-expr { font-family: "Times New Roman", Times, serif; font-style: italic; } .summary-box { background: #f8f9f9; border: 2px dashed #bdc3c7; padding: 20px; border-radius: 10px; margin-top: 40px; } .summary-box h3 { margin-top: 0; border-bottom: 1px solid #bdc3c7; padding-bottom: 10px; } @media (max-width: 600px) { .main-title-box { padding: 20px; } .main-title-box h1 { font-size: 22px; } .section-card { padding: 15px; } }

6th Maths : Term 1 Unit 3

Ratio and Proportion | Exercise 3.1

1. Fill in the blanks.

(i) Ratio of ₹ 3 to ₹ 5 = 3 : 5.

(ii) Ratio of 3m to 200 cm = 3 : 2. [Note: 200cm = 2m]

(iii) Ratio of 5 km 400 m to 6 km = 9 : 10. [Note: 54:60]

(iv) Ratio of 75 paise to ₹ 2 = 3 : 8. [Note: 75 : 200]

2. Say whether the following statements are True or False.

(i) The ratio of 130 cm to 1 m is 13 : 10. [True]

(ii) One of the terms in a ratio cannot be 1. [False]

3. Find the simplified form of the following ratios.

(i) 15 : 20 (ii) 32 : 24 (iii) 7 : 15 (iv) 12 : 27 (v) 75 : 100

Solution:

(i) 15 : 20
Fractional form = \( \frac{15 \div 5}{20 \div 5} = \frac{3}{4} \)
Simplest form = 3 : 4

(ii) 32 : 24
Fractional form = \( \frac{32 \div 8}{24 \div 8} = \frac{4}{3} \)
Simplest form = 4 : 3

(iii) 7 : 15
Fractional form = \( \frac{7}{15} \) (No common divisor)
Simplest form = 7 : 15

(iv) 12 : 27
Fractional form = \( \frac{12 \div 3}{27 \div 3} = \frac{4}{9} \)
Simplest form = 4 : 9

(v) 75 : 100
Fractional form = \( \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \)
Simplest form = 3 : 4

4. Akilan walks 10 km in an hour while Selvi walks 6 km in an hour. Find the simplest ratio of the distance covered by Akilan to that of Selvi.

Solution:

Distance Akilan walks in an hour = 10 km

Distance Selvi walks in an hour = 6 km

Ratio of distance covered by both = 10 : 6

Simplest form: \( \frac{10 \div 2}{6 \div 2} = \frac{5}{3} \)

Ratio of distance covered by Akilan and Selvi = 5 : 3

5. The cost of parking a bicycle is ₹ 5 and the cost of parking a scooter is ₹ 15. Find the simplest ratio of the parking cost of a bicycle to that of a scooter.

Solution:

Parking cost of a bicycle = ₹ 5

Parking cost of a scooter = ₹ 15

Simplest ratio of bicycle to scooter: \( \frac{5 \div 5}{15 \div 5} = \frac{1}{3} \)

Ratio of bicycle parking cost to scooter parking cost = 1 : 3

6. Out of 50 students in a class, 30 are boys. Find the ratio of

(i) number of boys to the number of girls.
(ii) number of girls to the total number of students.
(iii) number of boys to the total number of students.

Solution:

Total No. of students = 50

No. of boys = 30

No. of girls = 50 − 30 = 20 girls

(i) number of boys to the number of girls:
boys : girls = 30 : 20
Simplest form = \( \frac{30 \div 10}{20 \div 10} = \frac{3}{2} \)
Ratio = 3 : 2

(ii) number of girls to the total number of students:
girls : total students = 20 : 50
Simplest form = \( \frac{20 \div 10}{50 \div 10} = \frac{2}{5} \)
Ratio = 2 : 5

(iii) number of boys to the total number of students:
boys : total students = 30 : 50
Simplest form = \( \frac{30 \div 10}{50 \div 10} = \frac{3}{5} \)
Ratio = 3 : 5

Objective Type Questions

7. The ratio of ₹ 1 to 20 paise is __________.

(a) 1 : 5

(b) 1 : 2

(d) 5 : 1

Answer: (d) 5 : 1

8. The ratio of 1 m to 50 cm is __________.

(a) 1 : 50

(b) 50 : 1

(d) 1 : 2

Answer: (c) 2 : 1

9. The length and breadth of a window are 1m and 70 cm respectively. The ratio of the length to the breadth is __________.

(a) 1 : 7

(b) 7 : 1

(d) 10 : 7

Answer: (d) 10 : 7

10. The ratio of the number of sides of a triangle to the number of sides of a rectangle is:

(a) 4 : 3

(b) 3 : 4

(d) 3 : 2

Answer: (b) 3 : 4

11. If Azhagan is 50 years old and his son is 10 years old, then the simplest ratio between the age of Azhagan to his son is:

(a) 10 : 50

(b) 50 : 10

(d) 1 : 5

Answer: (c) 5 : 1

Quick Answers Summary:

1) (i) 3:5, (ii) 3:2, (iii) 9:10, (iv) 3:8

2) (i) True, (ii) False

3) (i) 3:4, (ii) 4:3, (iii) 7:15, (iv) 4:9, (v) 3:4

4) 5 : 3

5) 1 : 3

6) (i) 3:2, (ii) 2:5, (iii) 3:5

7) (d) 5:1 | 8) (c) 2:1 | 9) (d) 10:7 | 10) (b) 3:4 | 11) (c) 5:1