Worksheet Solutions: Proportional Reasoning-1 | Worksheets with Solutions for Class 8 PDF Download

Multiple Choice Questions (MCQs)

Q1. Simplify the ratio 56 : 72.
a) 14 : 18
b) 7 : 9
c) 28 : 36
d) 8 : 9
Answer: b) 7 : 9

Q2. If a : b = 2 : 3 and b : c = 3 : 5, then a : b : c = ?
a) 2 : 3 : 5
b) 2 : 3 : 9
c) 2 : 3 : 5
d) 2 : 3 : 7.5
Answer: a) 2 : 3 : 5

Q3. A sum of $600 is divided in the ratio 3 : 5. The smaller share is:
a) $225
b) $200
c) $250
d) $180
Answer: b) $225

Q4. If 6 pencils cost $24, the cost of 9 pencils is:
a) $28
b) $30
c) $36
d) $32
Answer: c) $36

Q5. The fourth proportion of 3, 9, and 12 is:
a) 27
b) 36
c) 24
d) 18
Answer: a) 27

Q6. The third proportion of 12 and 18 is:
a) 24
b) 27
c) 36
d) 30
Answer: b) 27

Fill in the Blanks

Q1: The ratio of 75 cm to 2.5 m is ___ : ___.
(Answer: 3 : 10)

Q2: If 4 pens cost $20, then the cost of 10 pens is ___.
(Answer: $50)

Q4: The ratio of 1 hour to 45 minutes is ___ : ___.
(Answer: 4 : 3)

Q5: If 7 : x = 21 : 63, then x = ___.
(Answer: 21)​

Q6: The third proportion of 8 and 12 is ___.
(Answer: 18)

Q7: If a : b = 5 : 7, then b : a = ___ : ___.
(Answer: 7 : 5)

Answer the following Questions: 

Q1. Simplify the ratio 42 : 63

Find HCF of 42 and 63 → HCF = 21

Divide both terms:
42 ÷ 21 = 2,   63 ÷ 21 = 3
Simplified ratio = 2 : 3

Q2. Ron gets 20% more marks than John. Find the ratio of their marks.

Let John’s marks = 100

Ron’s marks = 100 + 20% of 100 = 120

Ratio (Ron : John) = 120 : 100 = 6 : 5
Ratio = 6 : 5

Q3. Divide $490 in the ratio 4 : 3

Total parts = 4 + 3 = 7

Value of 1 part = 490 ÷ 7 = 70

• Shares:

• First part = 4 × 70 = 280

• Second part = 3 × 70 = 210
  Division = $280 and $210

Q4. A man distributes $4000 among three sons in the ratio 4 : 3 : 3. Find amount for first son.

Total parts = 4 + 3 + 3 = 10

Value of 1 part = 4000 ÷ 10 = 400

First son’s share = 4 × 400 = 1600
First son receives = $1600

Q5. If the ratio a : b = 2 : 3, and b : c = 3 : 4. Find the ratio a : c.

a : b = 2 : 3 → a = 2k, b = 3k

b : c = 3 : 4 → b = 3m, c = 4m

To combine, make b equal. LCM of 3 and 3 = 3
So, let b = 3 (common)
Then a = 2 (from first ratio), c = 4 (from second ratio)

Ratio a : c = 2 : 4 = 1 : 2

Answer: 1 : 2

Q6. Two numbers: Five times the first = Four times the second. Find ratio.

Let first = x, second = y

5x = 4y

x / y = 4 / 5

Ratio = 4 : 5

Answer: 4 : 5

Q7. Find the fourth proportion of 4, 9, and 12.

Fourth proportion = (9 × 12) ÷ 4
= 108 ÷ 4
= 27

Answer: 27 (option d)

Q8. Find the third proportion of 16 and 36.

Third proportion of a and b = (b²) ÷ a

Here a = 16, b = 36

Third proportion = (36²) ÷ 16
= 1296 ÷ 16
= 81