Practice Questions on Ratio and Proportion | Quantitative Techniques for CLAT PDF Download

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Q1: A car travels 240 miles in 4 hours. What is its average speed in miles per hour (mph)?
(a) 60      
(b) 40      
(c) 50    
(d) 70

Ans: (a)
Average Speed = Total Distance / Total Time
Average Speed = 240 miles / 4 hours
Average Speed = 60 mph

Q2: Two numbers are 30% and 20% less than a third number respectively. The ratio of first two numbers is:
(a) 7 : 6
(b) 3 : 2
(c) 7 : 8
(d) 8 : 7

Ans: (c)
Let the third number be 100.

First number = 100 - 30% of 100
First number = 100 - 30
First number = 70

Second number = 100 - 20% of 100
Second number = 100 - 20
Second number = 80

Ratio of the first two numbers = First number / Second number
⇒ Ratio = 70 / 80
⇒ Ratio = 7 / 8

The ratio of the first two numbers is 7 : 8.

Q3: A mixture contains sugar solution and colored water in the ratio of 4 : 3. If 10 liters of colored water is added to the mixture, the ratio becomes 4: 5. Find the initial quantity of sugar solution in the given mixture.
(a) 10    
(b) 20    
(c) 30    
(d) 40

Ans: (b)
The initial ratio is 4 : 3.
Let ‘k’ be the common ratio.
⇒ Initial quantity of sugar solution = 4 k
⇒ Initial quantity of colored water = 3 k
⇒ Final quantity of sugar solution = 4 k
⇒ Final quantity of colored water = 3 k + 10
Final ratio = 4 k : 3 k + 10 = 4 : 5
⇒ k = 5
Therefore, the initial quantity of sugar solution in the given mixture = 4 k = 20 liters

Q4: A invested Rs. 70,000 in a business. After a few months, B joined him with Rs. 60,000. At the end of the year, the total profit was divided between them in the ratio of 2: 1. After how many months did B join?                                            
(a) 5    
(b) 10    
(c) 15  
(d) 20

Ans: (a)
Let A work alone for ‘n’ months.
⇒ A’s input = 70,000 x 12
⇒ B’s input = 60,000 x (12 – n)
So, (70,000 x 12) / [60,000 x (12 – n)] = 2 / 1
⇒ (7 x 12) / [6 x (12 – n)] = 2 / 1
⇒ 12 – n = 7
⇒ n = 5
Therefore, B joined after 5 months.

Q5:  5 notebooks cost as much as 12 pens, 7 pens as much as 2 geometry, 3 geometry as much as 2 bottles. If the cost of 5 bottles is Rs 875, then find the cost of a notebook.
(a) 80  
(b) 85    
(c) 90  
(d) 95

Ans: (a)
5 bottles = 875
2 bottles = 875 * 2/5 = 3 geometry
2 geometry cost= 875 * 2/5 * 2/3 = 7 pens cost
12 pens cost = 875 * 2/5 * 2/3 * 12/7 = 5 notebook
1 notebook= 875 * 2/5 * 2/3 * 12/7 * 1/5 = Rs 80

Q6: What number must be subtracted from the numerator and denominator 43/37 that it becomes 3 : 2?
(a) 30  
(b) 25  
(c) 35  
(d) 20

Ans: (b)
Let x be the number subtracted from the fraction.
(43 – x) / (37 – x) = 3/2
86 – 2x = 111 – 3x
x = 25

Q7: The ratio of the ages of a father and his son is 5:2. If the father is 40 years older than the son, what are their ages(approximately)?
(a) 66,13 
(b) 76 ,14
(c) 86 ,13
(d) 56,12

Ans: (a)
Let the son’s age be “2x” years. Then, the father’s age is “5x” years.
According to the given information, the father is 40 years older than the son, so we can write the equation:
5x – 2x = 40
3x = 40
To find the value of “x,” divide both sides by 3:
x = 40 / 3 x = 13.33 (rounded to two decimal places)
So, the son’s age is approximately 13years,
and the father’s age is: 5x ≈ 5 * 13.33 ≈ 66 years(approximately)

Q8: In a mixture of milk and water, the ratio of milk to water is 5:2. If 8 liters of water are added to the mixture, the ratio becomes 5:3. How many liters of milk were in the original mixture?
(a) 10  
(b) 20  
(c) 30  
(d) 40

Ans: (d)
Milk = 5x liters 
Water = 2x liters
Now, when 8 liters of water are added, the ratio becomes 5:3. So, we have:
Milk = 5x liters 
Water = (2x + 8) liters
According to the new ratio, we can write:
5x / (2x + 8) = 5 / 3
=3 * 5x = 5 * (2x + 8)
=15x = 10x + 40
=5x = 40 = x = 8
Milk = 5x = 5 * 8 = 40 litres.

Q9: The ages of A, B, and C are in the ratio 5:7:9, and the sum of their ages is 63 years. How old is C?
(a) 25  
(b) 26  
(c) 27  
(d) 28

Ans: (c)
Let the ages of A, B, and C be 5x, 7x, and 9x, respectively, where x is a positive integer representing the common ratio.
According to the problem, the sum of their ages is 63 years: 5x + 7x + 9x = 63
21x = 63
x = 63 / 21
x = 3
Now that we know the value of x, we can find the age of C:
C’s age = 9x C’s age = 9 * 3
C’s age = 27 years

Q10: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B is-                        
(a) 4:3  
(b) 3:4  
(c) 2:4  
(d) 4:2

Ans: (a)
From the equation, we get
5% of A + 4% of B = 2/3 (6% of A + 8% of B)
⇒ 15% of A + 12% of B = 12% of A + 16% of B
⇒ [15 – 12] % of A = [16 – 12] % of B
⇒ 3 % of A = 4% of B
Therefore, A : B = 4 : 3.