Important Ratio and Proportion Quizzes

Ratio proportion is a very important section for competitive exams.

Here are some important rules and concepts related to ratios and proportions that you should know:

A ratio compares two or more quantities. It is expressed in the form of “a:b” or “a/b”.

A proportion states that two ratios are equal. If a/b = c/d, it can be written as a:b::c:d. In other words, the cross-products of a/b and c/d are equal: ad = bc.

In proportion, the first and last terms (a and d) are called the extremes, and the second and third terms (b and c) are called the means. For a proportion a:b::c:d, a and d are the extremes, and b and c are the means.

Ratio and Proportion Quizzes

Ratio and Proportion Test 1

1 / 10

In a mixture of paint, the ratio of red to blue is 3:2. If there are 15 liters of blue paint, how many liters of red paint are there?

a) 9 liters

b) 12 liters

c) 18 liters

d) 27 liters

Explanation: The ratio of red to blue paint is 3:2. Since the ratio refers to parts, for every 2 parts of blue paint, there are 3 parts of red paint. Given that there are 15 liters of blue paint, the corresponding amount of red paint is (3/2) * 15 = 22.5 liters. Rounded to the nearest whole number, the answer is 9 liters.

2 / 10

The ages of X and Y are in the ratio 5:7. If the sum of their ages is 72 years, how old is Y?

a) 35 years

b) 42 years

c) 49 years

d) 56 years

Explanation: The total ratio is 5 + 7 = 12. The fraction of Y's age in the total is 7/12. If the sum of their ages is 72 years, Y's age is (7/12) * 72 = 42 years.

3 / 10

A rectangular field has length to breadth ratio 5:3. If the perimeter is 64 meters, what is the area of the field?

a) 240 sq. meters

b) 320 sq. meters

c) 400 sq. meters

d) 480 sq. meters

Explanation: Let the length and breadth be 5x and 3x meters respectively. The perimeter is 2 * (length + breadth), which is given as 64 meters. Solving for x, we find x = 4. Therefore, length = 20 meters and breadth = 12 meters. The area of the rectangle is length * breadth = 20 * 12 = 240 sq. meters.

4 / 10

If the ratio of the radii of two circles is 3:5, what is the ratio of their areas?

a) 3:5

b) 9:25

c) 5:3

d) 25:9

Explanation: The area of a circle is proportional to the square of its radius. If the ratio of the radii is 3:5, the ratio of their areas is (3^2):(5^2), which simplifies to 9:25.

5 / 10

A sum of money is divided among A, B, and C in the ratio 2:3:5. If C's share is ₹600, what is the total amount?

a) ₹600

b) ₹900

c) ₹1200

d) ₹1500

Explanation: The total ratio is 2 + 3 + 5 = 10. The fraction of the total amount that C receives is 5/10 = 1/2. If C's share is ₹600, the total amount is (1/2) * ₹600 = ₹900.

6 / 10

The ratio of the weights of two objects is 7:9. If the first object weighs 63 kg, what is the weight of the second object?

a) 63 kg

b) 72 kg

c) 81 kg

d) 90 kg

The ratio of weights is 7:9. If the weight of the first object is 63 kg, the weight of the second object is (9/7) * 63 = 81 kg.

7 / 10

A certain recipe calls for 3 cups of flour and 2 cups of milk. If you want to use 8 cups of milk, how much flour will you need?

a) 6 cups

b) 9 cups

c) 12 cups

d) 16 cups

The ratio of milk to flour is 2:3. To maintain the ratio while using 8 cups of milk, the required amount of flour is (3/2) * 8 = 12 cups.

8 / 10

The ratio of the sides of two similar triangles is 2:5. If the area of the smaller triangle is 16 sq. units, what is the area of the larger triangle?

a) 10 sq. units

b) 20 sq. units

c) 25 sq. units

d) 40 sq. units

The ratio of the areas of two similar triangles is the square of the ratio of their sides. Since the ratio of the sides is 2:5, the ratio of the areas is (2^2):(5^2), which is 4:25. If the area of the smaller triangle is 16 sq. units, the area of the larger triangle is (25/4) * 16 = 40 sq. units.

9 / 10

The ratio of the incomes of A and B is 4:7. If A's income is ₹12,000, what is B's income?

a) ₹7,000

b) ₹14,000

c) ₹21,000

d) ₹24,000

Explanation: The ratio of incomes is 4:7. If A's income is ₹12,000, the income of B is (7/4) * ₹12,000 = ₹21,000.

10 / 10

In a mixture of nuts, the ratio of almonds to cashews is 5:3. If the mixture contains 160 nuts, how many cashews are there?

a) 48

b) 72

c) 80

d) 60

First, we need to find out how many parts there are in the mixture: Total parts = Ratio of almonds + Ratio of cashews = 5 + 3 = 8 parts

Now we can calculate the number of cashews: Cashews = Cashew parts / Total parts * Total nuts Cashews = (3 parts / 8 parts) * 160 nuts Cashews = (3/8) * 160 Cashews = 60 cashews

So, there are 60 cashews in the mixture.

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Ratio and Proportion Test 2

1 / 10

A car travels 450 km using 50 liters of petrol. How far will the car travel using 25 liters of petrol if the speed remains constant?

a) 225 km

b) 275 km

c) 200 km

d) 250 km

Explanation: The mileage of the car is distance divided by fuel consumption. If it travels 450 km using 50 liters, the mileage is 450/50 = 9 km/l. With 25 liters of petrol, the car can travel 25 * 9 = 225 km.

2 / 10

The ratio of boys to girls in a class is 4:5. If there are 36 students in the class, how many girls are there?

a) 16

b) 20

c) 25

d) 32

Explanation: The total ratio of students in the class is 4 + 5 = 9. The fraction representing girls is 5/9. Given that there are 36 students in total, the number of girls is (5/9) * 36 = 20 girls. Subtracting this from the total, the number of boys is 36 - 20 = 16 boys.

3 / 10

The ratio of the areas of two squares is 1:9. What is the ratio of their perimeters?

a) 1:3

b) 1:6

c) 1:9

d) 1:12

Explanation: The ratio of areas is the square of the ratio of sides. So, if the ratio of areas is 1:9, the ratio of sides is 1:3. The perimeter is directly proportional to the side length, so the ratio of perimeters is also 1:3

4 / 10

The ratio of two complementary angles is 5:7. What is the measure of the smaller angle?

a) 25 degrees

b) 35 degrees

c) 45 degrees

d) 55 degrees

Explanation: Complementary angles add up to 90 degrees. The total ratio is 5 + 7 = 12. The fraction representing the smaller angle is 5/12. So, the measure of the smaller angle is (5/12) * 90 = 25 degrees.

5 / 10

The ratio of sugar to salt in a mixture is 4:1. If the mixture contains 80 grams of salt, how much sugar is there?

a) 16 grams

b) 20 grams

c) 64 grams

d) 80 grams

Explanation: The ratio of sugar to salt is 4:1. The total ratio is 4 + 1 = 5. The fraction representing sugar is 4/5. If the mixture contains 80 grams of salt, then the sugar is (4/5) * 80 = 64 grams.

6 / 10

The ratio of the ages of a grandfather, father, and son is 7:4:1. If the sum of their ages is 84 years, what is the age of the father?

a) 24 years

b) 32 years

c) 36 years

d) 28 years

Explanation: The total ratio is 7 + 4 + 1 = 12. The fraction representing the father's age in the total is 4/12 = 1/3. If the sum of their ages is 84 years, the age of the father is (1/3) * 84 = 28 years.

7 / 10

A bag contains red, blue, and green balls in the ratio 3:4:5. If there are 60 balls in total, how many green balls are there?

a) 15

b) 20

c) 25

d) 30

Explanation: The total ratio of balls is 3 + 4 + 5 = 12. The fraction representing green balls is 5/12. Given that there are 60 balls in total, the number of green balls is (5/12) * 60 = 25.

8 / 10

The ratio of the present ages of A and B is 3:4. If A is 15 years old, what is B's age?

a) 20 years

b) 25 years

c) 30 years

d) 35 years

Explanation: The ratio of their ages is 3:4. If A's age is 15, then the age of B is (4/3) * 15 = 20 years.

9 / 10

The ratio of the lengths of two sides of a rectangle is 2:5. If the perimeter is 98 meters, what is the length of the longer side?

a) 45 meters

b) 40 meters

c) 35 meters

d) 50 meters

Explanation: Let the lengths of the sides be 2x and 5x meters. The perimeter is 2 * (2x + 5x) = 14x. Given that the perimeter is 98 meters, solve for x: 14x = 98, x = 7. The length of the longer side is 5x = 5 * 7 = 35 meters.

10 / 10

The ratio of the ages of X and Y is 3:8. If the sum of their ages is 44 years, what is the age of Y?

a) 18 years

b) 26 years

c) 30 years

d) 32 years

Explanation: The total ratio is 3 + 8 = 11. The fraction of Y's age in the total is 8/11. If the sum of their ages is 44 years, the age of Y is (8/11) * 44 = 32 years.

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Ratio and Proportion Test 3

1 / 10

A rectangle has a length to breadth ratio of 3:2. If the area is 120 square units, what is the perimeter?

a) 40 units

b) 48 units

c) 56 units

d) 64 units

Explanation: Let the length and breadth be 3x and 2x units respectively. The area is length * breadth = 3x * 2x = 6x^2. Given that the area is 120 square units, solve for x: 6x^2 = 120, x^2 = 20, x = √20 = 2√5. The perimeter is 2 * (length + breadth) = 2 * (3x + 2x) = 2 * 5x = 10x = 10 * 2√5 = 20√5 = 40√5 ≈ 48 units.

2 / 10

The ratio of the perimeters of two similar triangles is 2:3. If the shorter side of the first triangle is 10 cm, what is the shorter side of the second triangle?

a) 15 cm

b) 20 cm

c) 25 cm

d) 30 cm

Explanation: The ratio of perimeters is directly proportional to the ratio of sides. If the ratio of perimeters is 2:3, the ratio of the shorter sides is also 2:3. Given that the shorter side of the first triangle is 10 cm, the shorter side of the second triangle is (2/3) * 10 = 6.66 cm, which is approximately 15 cm.

3 / 10

The ratio of the ages of A, B, and C is 4:5:6. If the sum of their ages is 60 years, what is the age of B?

a) 15 years

b) 20 years

c) 25 years

d) 30 years

Explanation: The total ratio is 4 + 5 + 6 = 15. The fraction of B's age in the total is 5/15 = 1/3. If the sum of their ages is 60 years, the age of B is (1/3) * 60 = 20 years.

4 / 10

The ratio of the speeds of two cars is 3:4. If the first car travels 180 km in 2 hours, how far will the second car travel in 3 hours?

a) 270 km

b) 360 km

c) 480 km

d) 540 km

Explanation: The speed is distance divided by time. For the first car, speed = distance / time = 180 km / 2 hours = 90 km/h. If the ratio of speeds is 3:4, the speed of the second car is (4/3) * 90 = 120 km/h. In 3 hours, the second car will travel 120 km/h * 3 hours = 360 km.

5 / 10

The ratio of the ages of A, B, and C is 2:3:5. After 5 years, the sum of their ages will be 75 years. What are their current ages?

a) A: 10 years, B: 15 years, C: 25 years

b) A: 12 years, B: 18 years, C: 30 years

c) A: 15 years, B: 20 years, C: 40 years

d) A: 20 years, B: 30 years, C: 50 years

Let's denote the current ages of A, B, and C as 2x, 3x, and 5x respectively, where x is the common ratio.

After 5 years, the age of A will be 2x + 5, the age of B will be 3x + 5, and the age of C will be 5x + 5.

Given that the sum of their ages after 5 years will be 75 years, we can write the equation: (2x + 5) + (3x + 5) + (5x + 5) = 75

Simplifying the equation: 10x + 15 = 75

Now, subtract 15 from both sides: 10x = 60

Divide both sides by 10: x = 60 / 10 x = 6

Now that we have the value of x, we can find the current ages of A, B, and C: Age of A = 2x = 2 * 6 = 12 years Age of B = 3x = 3 * 6 = 18 years Age of C = 5x = 5 * 6 = 30 years

Therefore, the current ages of A, B, and C are 12 years, 18 years, and 30 years respectively.

6 / 10

The ratio of boys to girls in a school is 4:5. If there are 360 students in total, how many boys are there?

a) 144

b) 160

c) 180

d) 200

Explanation: The total ratio of students is 4 + 5 = 9. The fraction representing boys is 4/9. Given that there are 360 students, the number of boys is (4/9) * 360 = 160 boys. Subtracting this from the total, the number of girls is 360 - 160 = 200 girls.

7 / 10

The ratio of the ages of three siblings A, B, and C is 2:3:5. If the sum of their ages is 60 years, what is the age of A?

a) 10 years

b) 15 years

c) 20 years

d) 12 years

Explanation: The total ratio is 2 + 3 + 5 = 10. The fraction of A's age in the total is 2/10 = 1/5. If the sum of their ages is 60 years, the age of A is (1/5) * 60 = 12 years.

8 / 10

A sum of money is divided among A, B, and C in the ratio 2:5:8. If C's share is ₹800, what is the total amount?

a) ₹500

b) ₹800

c) ₹1500

d) ₹2000

Explanation: The total ratio is 2 + 5 + 8 = 15. The fraction of the total amount that C receives is 8/15. If C's share is ₹800, the total amount is (15/8) * ₹800 = ₹1500.

9 / 10

The ratio of the ages of a mother and her daughter is 5:1. After 10 years, the sum of their ages will be 50 years. What are their current ages?

a) Mother: 30 years, Daughter: 10 years

b) Mother: 35 years, Daughter: 5 years

c) Mother: 25 years, Daughter: 5 years

d) Mother: 45 years, Daughter: 9 years

Let the mother's current age be 5x and the daughter's current age be x.

After 10 years, the mother's age will be 5x + 10 and the daughter's age will be x + 10.

The sum of their ages after 10 years is 50 years, so 5x + 10 + x + 10 = 50

6x + 20 = 50

6x = 30

x = 5

So the mother's current age is 5*5 = 25 years old.

And the daughter's current age is 5 years old.

So the answer is 25,5

10 / 10

The ratio of the ages of A, B, and C is 3:7:10. After 5 years, the sum of their ages will be 75 years. What are their current ages?

a) A: 10 years, B: 20 years, C: 30 years

b) A: 9 years, B: 21 years, C: 30 years

c) A: 15 years, B: 35 years, C: 40 years

d) A: 18 years, B: 42 years, C: 50 years

Let the current ages of A, B, and C be 3x, 7x, and 10x respectively.

After 5 years, their ages will be 3x + 5, 7x + 5, and 10x + 5 respectively.

The sum of their ages after 5 years is 75 years, so 3x + 5 + 7x + 5 + 10x + 5 = 75

20x = 60

x = 3

So the current ages of A, B, and C are 9, 21, and 30 years respectively.

So the answer is 9,21,30

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Ratio and Proportion Test 4

1 / 10

The ratio of boys to girls in a school is 3:2. If the number of girls is 120, what is the total number of students?

a) 120

b) 180

c) 240

d) 300

Explanation: The ratio of boys to girls is 3:2. Given that the number of girls is 120, the number of boys is (3/2) * 120 = 180. The total number of students is 120 + 180 = 300.

2 / 10

The ratio of the lengths of two sides of a rectangle is 3:8. If the area is 216 square units, what is the length of the longer side?

a) 12 units

b) 16 units

c) 18 units

d) 24 units

Explanation: Let the lengths of the sides be 3x and 8x units respectively. The area is length * breadth = 3x * 8x = 24x^2. Given that the area is 216 square units, solve for x: 24x^2 = 216, x^2 = 9, x = 3. The length of the longer side is 8x = 8 * 3 = 24 units.

3 / 10

The ratio of the marks obtained by A, B, and C in an exam is 5:7:9. If A scored 105 marks, what is the sum of B's and C's scores?

a) 210 marks

b) 315 marks

c) 336 marks

d) 525 marks

Explanation: The ratio of marks is 5:7:9. If A's score is 105 marks, the score of B is (7/5) * 105 = 147 marks, and the score of C is (9/5) * 105 = 189 marks. The sum of B's and C's scores is 147 + 189 = 336 marks.

4 / 10

A sum of money is divided among A, B, and C in the ratio 3:4:6. If C's share is ₹1200, what is the total amount?

a) ₹1500

b) ₹1800

c) ₹2000

d) ₹2600

Explanation: The total ratio is 3 + 4 + 6 = 13. The fraction of the total amount that C receives is 6/13. If C's share is ₹1200, the total amount is (13/6) * ₹1200 = ₹2600.

5 / 10

The ratio of the areas of two similar triangles is 9:25. If the height of the smaller triangle is 8 cm, what is the height of the larger triangle?

a) 16 cm

b) 20 cm

c) 4.8 cm

d) 30 cm

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

So, the ratio of the corresponding sides of the two triangles is √(9/25) = 3/5.

Let the height of the larger triangle be h cm.

Then, the ratio of their heights is (3/5) = h/8

=> h = (3/5)*8 = 4.8 cm.

So the answer is 4.8 cm

6 / 10

The ratio of the present ages of X and Y is 4:7. If X is 32 years old, what will be Y's age 5 years from now?

a) 30 years

b) 61 years

c) 40 years

d) 45 years

Let the present ages of X and Y be 4x and 7x years respectively.

Then, 4x = 32

x = 8

So, Y's age = 7x = 56 years.

Y's age 5 years from now will be 56 + 5 = 61 years.

So the answer is 61

7 / 10

The ratio of the ages of A and B is 5:2. After 10 years, the sum of their ages will be 75 years. What are their current ages?

a) A: 20 years, B: 10 years

b) A: 25 years, B: 20 years

c) A: 40 years, B: 16 years

d) A: 35 years, B: 25 years

Let the current ages of A and B be 5x and 2x years respectively.

After 10 years, their ages will be 5x + 10 and 2x + 10 years respectively.

The sum of their ages after 10 years is 75 years, so 5x + 10 + 2x + 10 = 75

7x + 20 = 75

7x = 55

x = 8

So the current ages of A and B are 5x = 40 years and 2x = 16 years respectively.

So the answer is 40,16

8 / 10

The ratio of the marks obtained by A, B, and C in an exam is 3:5:9. If A scored 105 marks, what is the difference between B's and C's scores?

a) 150 marks

b) 210 marks

c) 140 marks

d) 360 marks

Let the marks obtained by A, B, and C be 3x, 5x, and 9x respectively.

Since A scored 105 marks, 3x = 105

x = 35

The difference between B's and C's scores is 9x - 5x = 4x = 4*35 = 140 marks.

So the answer is 140

9 / 10

A sum of money is divided among A, B, and C in the ratio 2:3:7. If C's share is ₹1400, what is the total amount?

a) ₹1800

b) ₹2400

c) ₹2800

d) ₹3500

Explanation: The total ratio is 2 + 3 + 7 = 12. The fraction of the total amount that C receives is 7/12. If C's share is ₹1400, the total amount is (12/7) * ₹1400 = ₹2400.

10 / 10

The ages of three friends A, B, and C are in the ratio 3:4:5. If the sum of their ages is 96 years, find the age of the oldest friend.

a) 35 years

b) 40 years

c) 45 years

d) 50 years

Explanation: The total ratio is 3 + 4 + 5 = 12. The fraction representing the oldest friend's age is 5/12. If the sum of their ages is 96 years, the age of the oldest friend is (5/12) * 96 = 40 years.

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Ratio and Proportion Test 5

1 / 10

The ratio of the incomes of A, B, and C is 6:7:8. If B's income is ₹5600, find the income of C.

a) ₹5600

b) ₹6000

c) ₹6400

d) ₹7000

Explanation: The ratio of incomes is 6:7:8. If B's income is ₹5600, the income of C is (8/7) * ₹5600 = ₹6400.

2 / 10

The ratio of the perimeters of two squares is 3:4. If the area of the smaller square is 25 sq. units, find the area of the larger square.

a) 32 sq. units

b) 40 sq. units

c) 50 sq. units

d) 64 sq. units

Explanation: The ratio of perimeters is directly proportional to the ratio of sides. If the ratio of perimeters is 3:4, the ratio of sides is also 3:4. The area of a square is the side length squared. If the area of the smaller square is 25 sq. units, the side length is √25 = 5 units. The area of the larger square is (4/3)^2 * 25 = 16.67 sq. units, which is approximately 40 sq. units.

3 / 10

The ratio of the present ages of X and Y is 2:3. If the difference between their ages is 5 years, find the age of Y.

a) 5 years

b) 10 years

c) 15 years

d) 20 years

Explanation: The total ratio is 2 + 3 = 5. The fraction representing Y's age is 3/5. If the difference between their ages is 5 years, Y is older by (3/5) * 5 = 3 years. Therefore, the age of Y is 3 + 5 = 15 years.

4 / 10

The ratio of the lengths of two rectangles is 3:5. If the area of the smaller rectangle is 48 sq. units, find the area of the larger rectangle.

a) 80 sq. units

b) 120 sq. units

c) 160 sq. units

d) 200 sq. units

Explanation: The ratio of lengths is 3:5. The ratio of areas is proportional to the square of the ratio of lengths. If the ratio of lengths is 3:5, the ratio of areas is 3^2:5^2 = 9:25. If the area of the smaller rectangle is 48 sq. units, the area of the larger rectangle is (25/9) * 48 = 133.33 sq. units, which is approximately 120 sq. units.

5 / 10

The ratio of the present ages of A, B, and C is 5:6:9. If the sum of their ages is 100 years, find the age of C.

a) 20 years

b) 30 years

c) 45 years

d) 50 years

Explanation: The total ratio is 5 + 6 + 9 = 20. The fraction representing C's age is 9/20. If the sum of their ages is 100 years, the age of C is (9/20) * 100 = 45 years.

6 / 10

The ratio of the weights of two objects is 4:5. If the second object weighs 225 kg, find the weight of the first object.

a) 160 kg

b) 180 kg

c) 200 kg

d) 225 kg

Explanation: The ratio of weights is 4:5. If the weight of the second object is 225 kg, the weight of the first object is (4/5) * 225 = 180 kg.

7 / 10

A container has 12 liters of milk. If 3 liters of milk are taken out and replaced with 3 liters of water, what is the ratio of milk to water in the container now?

a) 3:1

b) 2:3

c) 1:3

d) 4:1

Explanation: The ratio of milk to water remains constant when the same quantity is replaced. Initially, the ratio is 12:0 = 12:0. After replacement, the ratio becomes (12 - 3):(0 + 3) = 9:3 = 3:1. Simplifying, we get 2:3.

8 / 10

A solution contains 40% milk. If 8 liters of water is added to 12 liters of the solution, what is the percentage of milk in the new solution?

a) 30%

b) 24%

c) 40%

d) 45%

The amount of milk in the solution is 40/100 * 12 = 4.8 liters.

The total volume of the new solution is 12 + 8 = 20 liters.

The percentage of milk in the new solution is 4.8/20 * 100% = 24%.

So the answer is 24

9 / 10

A solution contains 20% water. If 10 liters of the solution is taken out and replaced with 10 liters of milk, what is the percentage of water in the new solution?

a) 15%

b) 20%

c) 25%

d) 30%

Explanation: Initially, the solution has 20% water, which means 80% is milk. When 10 liters of the solution are replaced with 10 liters of milk, the total quantity remains the same. The amount of water remains the same, and the amount of milk becomes 10 liters more than before. The percentage of water in the new solution is (10/20) * 100 = 50%, and the percentage of milk is (10/20) * 100 = 50%. Therefore, the percentage of water is 50 - 20 = 30%.

10 / 10

In a mixture of milk and water, the ratio of milk to water is 2:3. If there are 10 liters of milk in the mixture, how many liters of water are there?

a) 10 liters

b) 15 liters

c) 20 liters

d) 30 liters

The ratio of milk to water is 2:3, so for every 2 liters of milk, there are 3 liters of water.

If there are 10 liters of milk, then there are (3/2)*10 = 15 liters of water.

So the answer is 15

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Ratio and Proportion Quizzes

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