Ratio and Proportion

Multiple Choice Questions (MCQ)

1. Which of the following is a correct simplified form of the ratio 75 cm : 1.5 m?
A. 1 : 2
B. 2 : 3
C. 1 : 3
D. 1 : 1
Answer: A. 1 : 2
(Convert 1.5 m = 150 cm ⇒ 75 : 150 = 1 : 2)

2. If a : b = 2 : 5 and b : c = 3 : 4, what is the compound ratio of a : c?
A. 6 : 20
B. 6 : 25
C. 2 : 4
D. 5 : 6
Answer: B. 6 : 25
(a : b = 2 : 5, b : c = 3 : 4 → b common = 15 ⇒ a : b = 6 : 15, b : c = 15 : 20 ⇒ a : c = 6 : 25)

3. Which of the following sets of numbers is in continued proportion?
A. 3, 6, 12
B. 5, 10, 15
C. 2, 4, 8
D. 1, 3, 9
Answer: C. 2, 4, 8
(Check: 4² = 16 and 2×8 = 16 ⇒ continued proportion)

4. If a : b = c : d, then which of the following is true by the Alternendo Rule?
A. a : c = b : d
B. a + b = c + d
C. a : d = b : c
D. a × d = b × c
Answer: A. a : c = b : d
(Alternendo Rule: If a : b = c : d, then a : c = b : d)

5. If the ratio of two numbers is 4:5 and their sum is 81, what is the smaller number?
A. 35
B. 36
C. 45
D. 48
Answer: B. 36
(4 + 5 = 9 parts; each part = 81 ÷ 9 = 9 ⇒ smaller number = 4 × 9 = 36)

Short Answer Questions (SAQ)

1. Simplify the ratio 500 ml : 2 L.
Answer: Convert 2 L = 2000 ml ⇒ 500 : 2000 = 1 : 4

2. If a : b = 3 : 4, find the duplicate ratio.
Answer: Duplicate ratio = a² : b² = 3² : 4² = 9 : 16

3. Check whether 6, 12, 24 are in continued proportion.
Answer: Middle term² = 12² = 144
Product of extremes = 6 × 24 = 144 ⇒ Yes, in continued proportion.

Long Answer Questions (LAQ)

1. If A : B = 2 : 3 and B : C = 4 : 5, find A : B : C.
Answer: A : B = 2 : 3
B : C = 4 : 5
Make B common: LCM of 3 and 4 = 12
A : B = 8 : 12
B : C = 12 : 15
⇒ A : B : C = 8 : 12 : 15

2. A sum of ₹840 is divided among A, B, and C in the ratio 2:3:4. Find each person’s share.
Answer: Total parts = 2 + 3 + 4 = 9 parts
Each part = ₹840 ÷ 9 = ₹93.33 (recurring)
A’s share = 2 × 93.33 = ₹186.67
B’s share = 3 × 93.33 = ₹280
C’s share = 4 × 93.33 = ₹373.33
(Accept rounding to nearest paise if required)

Ratio and Proportion