Unit Test (Solutions): Proportional Reasoning-1 | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

Time: 1 hour
M.M.: 30

General Instructions:

• Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.

• Question numbers 6 to 8 carry 2 marks each.

• Question numbers 9 to 11 carry 3 marks each.

• Question numbers 12 and 13 carry 5 marks each.

Q1. Simplify the ratio 84 : 126.
a) 4 : 5
b) 2 : 3
c) 6 : 9
d) 7 : 10
Answer: b) 2 : 3

Q2. If a : b = 3 : 4 and b : c = 2 : 5, then a : b : c = ?
a) 6 : 8 : 20
b) 3 : 4 : 5
c) 2 : 3 : 5
d) 5 : 10 : 8
Answer: a) 6 : 8 : 20

Q3. A sum of $720 is divided in the ratio 2 : 7. The smaller share is:
a) $160
b) $140
c) $200
d) $180
Answer: b) $160

Q4. If 8 notebooks cost $64, the cost of 5 notebooks is:
a) $30
b) $35
c) $40
d) $45
Answer: c) $40

Q5. The fourth proportion of 5, 10, and 15 is:
a) 20
b) 25
c) 30
d) 35
Answer: b) 25

Q6. Fill in the Blanks: 

(a) The ratio of 2.5 m to 75 cm is ___ : ___.
(b) If 7 pencils cost $21, then the cost of 12 pencils is ___.
(c) If 9 : x = 27 : 54, then x = ___.

Ans: (a) 10 : 3

(b) $36

(c) 18

Q7: The monthly incomes of P and Q are in the ratio 5 : 7. If Q’s income is ₹42,000, find P’s income.

Solution:
Ratio P : Q = 5 : 7
So, 5 : 7 :: x : 42000

Cross multiply:
5 × 42000 = 7 × x
210000 = 7x
x = 210000 ÷ 7 = 30000

Answer: P’s income = ₹30,000

Q8: A recipe needs oil and milk in the ratio 4 : 3. If you use 900 g of milk, how much oil is needed?

Solution:
Oil : Milk = 4 : 3
So, 4 : 3 :: x : 900

Cross multiply:
4 × 900 = 3 × x
3600 = 3x
x = 3600 ÷ 3 = 1200

Answer: Oil needed = 1200 g (1.2 kg)

Q9. Simplify the ratio 90 : 135.
Solution:
HCF of 90 and 135 = 45
90 ÷ 45 = 2, 135 ÷ 45 = 3
Simplified ratio = 2 : 3

Q10. A’s salary is 25% more than B’s salary. Find the ratio of A’s salary to B’s salary.
Solution:
Let B’s salary = 100
A’s salary = 100 + 25 = 125
Ratio A : B = 125 : 100 = 5 : 4

Q11. Divide $630 in the ratio 5 : 4.
Solution:
Total parts = 9
Value of 1 part = 630 ÷ 9 = 70
Shares: 5 × 70 = 350, 4 × 70 = 280
Answer: $350 and $280

Q12. A man distributes $5400 among three daughters in the ratio 3 : 2 : 1. Find the amount received by each.
Solution:
Total parts = 3 + 2 + 1 = 6
Value of 1 part = 5400 ÷ 6 = 900
Daughter 1 = 3 × 900 = 2700
Daughter 2 = 2 × 900 = 1800
Daughter 3 = 1 × 900 = 900
Answer: $2700, $1800, $900

Q13. If a : b = 4 : 5 and b : c = 10 : 7, find the ratio a : b : c.
Solution:
a : b = 4 : 5 → a = 4k, b = 5k
b : c = 10 : 7 → b = 10m, c = 7m
To combine, make b equal.
LCM of 5 and 10 = 10
So, let b = 10 → a = 8, c = 7
Ratio = 8 : 10 : 7