Practice Test on Ratio and Proportion helps students to get knowledge on different levels. The Ratio and Proportion Questions and Answers provided range from beginner, medium, hard levels. Practice the Questions here and get to know how to solve different problems asked. All the Ratio and Proportion Word Problems covered are as per the latest syllabus. Master the topic of Ratio and Proportion by practicing the Problems on a consistent basis and score better grades in your exam.
Ratio and Proportion Questions and Answers
1. The ratio of monthly income to the savings in a family is 5 : 3 If the savings be $6000, find the income and the expenses?
Solution:
Let us assume the Income be 5x
whereas savings be 3x
Given Savings = $6000
3x = 6000
x = 6000/3
= 2000
Income = 5x
= 5*2000
= $10,000
Expenses = Income – Savings
= 5x – 3x
= 2x
= 2*2000
= $4000
Therefore, Income and Expenses are $10,000 and $ 4000.
2. Two numbers are in the ratio 7: 4. If 3 is subtracted from each of them, the ratio becomes 5 : 2. Find the numbers?
Solution:
Let us consider the number be x
so 7x:4x
If 3 is subtracted the ratio becomes 5:2 then we have
7x-3:4x-3 = 5:2
equating them ad solving we get the values as
7x-3/4x-3 = 5/2
(7x-3)2 = 5(4x-3)
14x-6 = 20x-15
-6+15 = 20x-14x
9 = 6x
6x = 9
x = 9/6
= 3/2
Therefore the numbers are 7(3/2) and 4(3/2)
= 21/2, 6
3. Two numbers are in the ratio 3 : 5. If their sum is 720, find the numbers?
Solution:
Let us consider the number be x
Therefore two numbers become 3x:5x
Since their Sum = 720
3x+5x = 720
8x = 720
x = 720/8
= 90
Numbers are 3x and 4x
Thus, they become 3(90) and 4(90) i.e. 270 and 360.
4. A sum of money is divided among Rohan and Anand in the ratio 4 : 6. If Anand’s share is $600, find the total money?
Solution:
Let the money be x
Rohan and Anand’s Share = 4x:6x
Anand’s Share = $600
6x = $600
x = $100
Rohan’s Share = 4x
= 4*100
= $400
Total Money = Rohan’s Share + Anand’s Share
= $400+$600
= $1000
Therefore, the Sum of Money is $1000
5. The difference between the two numbers is 33 and the ratio between them is 5 : 2. Find the numbers?
Solution:
Let the number be x
From the given data
we have 5x-2x = 33
3x = 33
x = 11
Numbers are 5x, 2x
thus, they become 5*11 and 2*11
= 55, 22
Therefore, the numbers are 55 and 22.
6. The ages of A and B are in the ratio 3 : 6. Four years later, the sum of their ages is 53. Find their present ages?
Solution:
Let the Present Ages be 3x and 6x
After four Years Age of A and B Becomes 3x+4 and 6x+4
We know sum of their ages after 4 years = 53
3x+4+6x+4 = 53
9x+8 = 53
9x = 53-8
9x = 45
x =5
Present Ages of A and B is 3x and 6x
thus 3*5 and 6*5 i.e. 15 and 30
Therefore, the Present Ages of A and B are 15 and 30.
7. If 3A = 4B = 5C, find the ratio of A : B : C?
Solution:
Let us assume that 3A = 4B = 5C = k
Equating them we have A = k/3, B = k/4, C = k/5
Therefore, Ratio becomes = k/3:k/4:k/5
LCM of 3, 4, 5 is 60
Thus expressing them in terms of least common multiple we have
A:B:C = 20:15:12
Therefore, Ratio of A:B:C is 20:15:12
8. A certain sum of money is divided among a, b, c in the ratio 3:4:5. of a share is $300, find the share of b and c?
Solution:
Let us consider the sum of money as x
Since it is shared among the ratio of 3:4:5 we have 3x:4x:5x
We know a’s share is 3x = $300
x =$100
Share of b = 4x
= 4*100
= $400
Share of C = 5x
= 5*100
= $500
9. Divide $900 among A, B, C in the ratio 3: 4 ∶ 5?
Solution:
Let us assume the total money as x
Since the sum is to be shared among A, B, C in the ratio of 3:4:5 we have
3x+4x+5x = $900
12x = $900
x = $900/12
=$75
Share of A = 3x
= 3*75
= $225
Share of B = 4x
= 4*75
= $300
Share of C = 5x
= 5*75
= $375
10. Find the first term, if second, third, and fourth terms are 21, 80, 120?
Solution:
Let the Terms be a, a+d, a+2d, a+3d
Given Second Term = 21
a+d = 21
Third Term = 80
a+2d = 80
Fourth Term = 120
a+3d = 120
Using the Eliminating Method
a+d = 21
a+2d = 80
_______
Subtracting them we get the value of d as
-d = -59
d= 59
Substitute the value of d in any of the terms
a+d = 21
a+59 =21
a =21-59
= -38