Notes For Ratio and Proportion

 Notes Based On Ratio And Proportion Based On CUET , CLAT and IPMAT:

Ratio:

Definition: A ratio is a comparison of two quantities.

 

Types of Ratios:

1. Simple Ratio: A ratio expressed in the form a:b.

Example: 3:4

 

2. Compound Ratio: A ratio expressed as a combination of two or more simple ratios.

Example: 2:3 = 4:6

 

1. Proportional Ratio: A ratio that remains constant.

Example: 2:3 = 4:6 = 6:9

 

Properties of Ratios:

1. Commutative Property: a:b = b:a

2. Associative Property: (a:b) : (c:d) = a:c : b:d

3. Distributive Property: a:(b+c) = a:b + a:c

 

Proportion

 

Definition: A proportion is an equation that states that two ratios are equal.

 

Types of Proportions:

 

1. Direct Proportion: As one quantity increases, the other quantity also increases.

Example: 2:3 = 4:6

2. Indirect Proportion: As one quantity increases, the other quantity decreases.

Example: 2:3 = 6:4

 

Properties of Proportions:

 

1. Transitive Property: If a:b = c:d and c:d = e:f, then a:b = e:f

2. Inverse Property: If a:b = c:d, then b:a = d:c

 

Key Concepts:

1. Ratio and Proportion Formula: (a:b) = (c:d) => ad = bc

2. Means and Extremes: a:b = c:d => a+c = b+d (means), a+d = b+c (extremes)

3. Third and Fourth Proportional:

    - Third Proportional: a:b = c:d => b/a = d/c

    - Fourth Proportional: a:b = c:d => a/c = b/d

4. Division of Quantity: Divide a quantity in a given ratio.

 

Solved Examples:

1. If 6:8 = x:12, find x.

Solution: 6/8 = x/12 => x = 9

 

2. Divide 30 in ratio 2:3.

Solution: 2/5 * 30 = 12, 3/5 * 30 = 18

 

3. Find the third proportional to 8:12.

Solution: 8/12 = x/24 => x = 16

 

Practice Questions:

1. If 3:5 = x:15, find x.

2. Divide 48 in ratio 5:7.

3. Find the fourth proportional to 6:8.

4. If 9:12 = x:16, find x.

 

Tips and Tricks:

 

1. Simplify ratios before solving.

2. Use algebraic methods to solve complex problems.

3. Check for direct or indirect proportion.

4. Practice variety of problems.

 

Importance in CUET, CLAT, and IPMAT:

 

1. Ratio and Proportion concepts are tested in Quantitative Ability sections.

2. Questions may involve simple or compound ratios, direct or indirect proportions.

3. Ability to apply concepts to solve problems is crucial.

 

Common Errors:

 

1. Incorrect simplification of ratios.

2. Confusing direct and indirect proportions.

3. Incorrect application of formulas.

 

 

Here are the last 5 years' questions based on Ratio and Proportion for CUET, CLAT, and IPMAT, along with solutions:

 

CUET :

 

1. 2022: If 5:7 = x:21, find x.

 

Solution: 5/7 = x/21 => x = (5/7) * 21 => x = 15

 

2. 2021: Divide 120 in ratio 2:3:5.

 

Solution: Total parts = 2+3+5 = 10

Part 1 = 2/10 * 120 = 24

Part 2 = 3/10 * 120 = 36

Part 3 = 5/10 * 120 = 60

 

3. 2020: Find the third proportional to 9:12.

 

Solution: 9/12 = x/24 => x = (9/12) * 24 => x = 18

 

4. 2019: If 3:5 = x:25, find x.

 

Solution: 3/5 = x/25 => x = (3/5) * 25 => x = 15

 

5. 2018: A sum of money is divided among A, B, and C in ratio 2:3:5. If C gets ₹750, find the share of B.

 

Solution: Total parts = 2+3+5 = 10

C's share = 5/10 = 750

B's share = 3/10 = (3/5) * 750 => B's share = 450

 

CLAT

 

1. 2022: If 2:3 = x:12, find x.

 

Solution: 2/3 = x/12 => x = (2/3) * 12 => x = 8

 

2. 2021: A, B, and C start a business with investments in ratio 5:7:9. If C's investment is ₹9000, find B's investment.

 

Solution: Total parts = 5+7+9 = 21

C's investment = 9/21 * 9000 = 9000

B's investment = 7/21 * 9000 => B's investment = 6000

 

3. 2020: Divide 48 in ratio 3:5.

 

Solution: Total parts = 3+5 = 8

Part 1 = 3/8 * 48 = 18

Part 2 = 5/8 * 48 = 30

 

4. 2019: Find the fourth proportional to 8:12.

 

Solution: 8/12 = x/24 => x = (8/12) * 24 => x = 16

 

5. 2018: If 9:12 = x:16, find x.

 

Solution: 9/12 = x/16 => x = (9/12) * 16 => x = 12

 

IPMAT

 

1. 2022: If 3:5 = x:25, find x.

 

Solution: 3/5 = x/25 => x = (3/5) * 25 => x = 15

 

2. 2021: A bag contains ₹120 in coins of denominations ₹5, ₹2, and ₹1 in ratio 6:4:3. Find the number of ₹5 coins.

 

Solution: Total parts = 6+4+3 = 13

₹5 coins = 6/13 * 120 = 55.38 (round to 55 coins)

 

3. 2020: Find the mean proportional between 9 and 16.

 

Solution: √(9*16) = √144 = 12

 

3. 2019: Divide 240 in ratio 2:3:5.

 

Solution: Total parts = 2+3+5 = 10

Part 1 = 2/10 * 240 = 48

Part 2 = 3/10 * 240 = 72

Part 3 = 5/10 * 240 = 120

 

4. 2018: If 2:3 = x:9, find x.

 

Solution: 2/3 = x/9 => x = (2/3) * 9 => x = 6

 

 

Some Important MCQs based on Ratio and Proportion for CUET , CLAT and IPMAT

 

1. If 2:3 = x:12, then x = ?

A) 6

B) 8

C) 10

D) 12

 

Answer: B) 8

 

2. Divide 120 in ratio 2:3:5. What is Part 2?

A) 24

B) 36

C) 48

D) 60

 

Answer: B) 36

 

3. Find the third proportional to 9:12.

A) 16

B) 18

C) 20

D) 24

 

Answer: B) 18

 

4. If 3:5 = x:25, then x = ?

A) 12

B) 15

C) 18

D) 20

Answer: B) 15

 

5. A sum of money is divided among A, B, and C in ratio 2:3:5. If C gets ₹750, find B's share.

A) ₹400

B) ₹450

C) ₹500

D) ₹600

 

Answer: B) ₹450

 

6. If 5:7 = x:21, then x = ?

A) 12

B) 15

C) 18

D) 20

 

Answer: B) 15

 

7. Find the mean proportional between 9 and 16.

A) 10

B) 12

C) 14

D) 16

 

Answer: B) 12

 

8. Divide 240 in ratio 2:3:5. What is Part 3?

A) 48

B) 72

C) 96

D) 120

 

Answer: D) 120

 

9. If 2:3 = x:9, then x = ?

A) 4

B) 6

C) 8

D) 10

 

Answer: B) 6

 

10. A bag contains ₹120 in coins of denominations ₹5, ₹2, and ₹1 in ratio 6:4:3. How many ₹5 coins are there?

A) 40

B) 48

C) 55

D) 60

 

Answer: C) 55

 

11. If 3:4 = x:16, then x = ?

A) 9

B) 12

C) 15

D) 18

 

Answer: B) 12

 

12. Find the fourth proportional to 8:12.

A) 12

B) 16

C) 20

D) 24

 

Answer: B) 16

 

13. Divide 180 in ratio 3:5. What is Part 1?

A) 36

B) 45

C) 54

D) 72

 

Answer: B) 45

 

14. If 5:6 = x:18, then x = ?

A) 12

B) 15

C) 18

D) 20

 

Answer: B) 15

 

15. A sum of money is divided among A, B, and C in ratio 3:5:7. If C gets ₹2100, find A's share.

A) ₹900

B) ₹1200

C) ₹1500

D) ₹1800

 

Answer: A) ₹900

 

16. Find the third proportional to 12:16.

A) 20

B) 24

C) 28

D) 32

 

Answer: B) 24

 

17. If 2:5 = x:25, then x = ?

A) 8

B) 10

C) 12

D) 15

 

Answer: B) 10

 

18. Divide 300 in ratio 2:3:5. What is Part 2?

A) 60

B) 90

C) 120

D) 150

 

Answer: B) 90

 

19. Find the mean proportional between 16 and 25.

A) 18

B) 20

C) 22

D) 24

 

Answer: B) 20

 

20. If 3:4 = x:12, then x = ?

A) 6

B) 8

C) 9

D) 12

 

Answer: B) 9

 

 

20. If 3:4 = x:12, then x = ?

A) 6

B) 8

C) 9

D) 12

 

Answer: C) 9

 

21. A bag contains ₹240 in coins of denominations ₹10, ₹5, and ₹2 in ratio 4:6:8. How many ₹5 coins are there?

A) 30

B) 36

C) 40

D) 48

 

Answer: B) 36

 

22. Divide 360 in ratio 2:3:5. What is Part 3?

A) 90

B) 120

C) 150

D) 180

 

Answer: C) 150

 

23. Find the fourth proportional to 12:16.

A) 16

B) 20

C) 24

D) 28

 

Answer: C) 24

 

24. If 5:7 = x:21, then x = ?

A) 12

B) 15

C) 18

D) 20

 

Answer: B) 15

 

25. A sum of money is divided among A, B, and C in ratio 3:5:7. If C gets ₹3150, find B's share.

A) ₹1500

B) ₹1750

C) ₹2000

D) ₹2250

 

Answer: B) ₹1750

 

26. Find the mean proportional between 25 and 49.

A) 30

B) 35

C) 40

D) 45

 

Answer: B) 35

 

27. If 2:3 = x:9, then x = ?

A) 4

B) 6

C) 8

D) 10

 

Answer: B) 6

 

28. Divide 420 in ratio 3:5:7. What is Part 2?

A) 105

B) 140

C) 175

D) 210

 

Answer: B) 140

 

29. Find the third proportional to 15:20.

A) 24

B) 28

C) 32

D) 36

 

Answer: B) 28

 

30. If 3:5 = x:25, then x = ?

A) 12

B) 15

C) 18

D) 20

 

Answer: B) 15