Olympiad Test: Ratio & Proportion - Class 6 MCQ

We are asked to identify the ratio of 4 seconds and 1/4 minute. Let's break it down:

1 minute = 60 seconds, so:

1/4 minute = 1/4 × 60 = 15 seconds

Now, the ratio of 4 seconds to 15 seconds is:

Ratio = 4 : 15

The dimensions of the poster are:

• Length = 1.5 cm
• Width = 7.5 cm

The perimeter of a rectangle is given by the formula:

Perimeter = 2 × (Length + Width)

Substitute the values:

Perimeter = 2 × (1.5 + 7.5) = 2 × 9 = 18 cm

Now, the ratio of the length to the perimeter is:

Ratio = Length / Perimeter = 1.5 / 18 = 1 / 12

Final Answer:

The ratio of the length to the perimeter is 1 : 12.

Thus, the correct answer is B: 1 : 12.

To determine the ratio of the length and width of the tape, we first need to ensure both measurements are in the same unit. The length is given as 2 meters, and the width is given as 28 centimeters

1. Convert the length from meters to centimeters. Since 1 meter is equal to 100 centimeters, we have:
   Length (in cm) = 2m × 100cm/m = 200cm

2. Now that both measurements are in centimeters, we can express the ratio of length to width:
   Ratio = Length/Width ​= 200cm​/28cm

3. Simplify the ratio. To do this, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 200 and 28 is 4:
   

This gives us the simplified ratio of length to width as 50 : 7

Therefore, the correct answer is option A, which corresponds to the ratio 50 : 7

The given ratio is 3 : 8, where:

• The antecedent is 3
• The consequent is 8

To find the new ratio, we add 4 to the antecedent and 2 to the consequent:

• New antecedent = 3 + 4 = 7
• New consequent = 8 + 2 = 10

Therefore, the new ratio is 7 : 10, which matches D: 7 : 10.

The total number of children in the coaching camp is 1200, and the number of children selected for various matches is 900.

Therefore, the number of non-selected children is:

Non-selected children = 1200 - 900 = 300

Now, the ratio of non-selected children to the total number of children is:

Ratio = Non-selected children / Total children = 300 / 1200

Simplifying the ratio:

300 / 1200 = 1 / 4

Answer: The correct ratio is 1 : 4, which corresponds to option C: 1 : 4.

For two ratios to be equal, the product of the means must be equal to the product of the extremes. This is the condition for the equality of two ratios.

For example, if we have two ratios:

a / b = c / d

The condition for equality is:

a * d = b * c

This is known as the "cross-multiplication" rule, and it means that the product of the means (b and c) is equal to the product of the extremes (a and d).

Answer: The correct answer is D: Product of means is equal to product of extremes.

In a proportion of the form a : b = c : d, the extremes are the first and the last terms, i.e., a and d.

For the proportion 9 : 3 :: 36 : 12, the extremes are:

• a = 9 (the first term)
• d = 12 (the last term)

Thus, the extremes of the proportion 9 : 3 :: 36 : 12 are 9 and 12.

Answer: The correct answer is D: 9, 12.

The given proportion is 12 : 3 = x : 1. To solve for x, we use the property of proportions where the product of the extremes is equal to the product of the means.

So, we have:

12 * 1 = 3 * x

This simplifies to:

12 = 3x

Now, solve for x:

x = 12 / 3 = 4

Therefore, the value of x is 4.

Answer: The correct answer is C: 4.

A proportion is an equation that states that two ratios are equal. In the form a : b = c : d, the product of the extremes must be equal to the product of the means:

a * d = b * c

Checking each option:

Option A: 3, 27, 9, 9

Checking the cross product:

3 * 9 = 27

This is not a proportion because the cross products are not equal.

Option B: 5, 11, 15, 44

Checking the cross product:

5 * 44 = 220 and 11 * 15 = 165

This is not a proportion because the cross products are not equal.

Option C: 3, 5, 15, 25

Checking the cross product:

3 * 25 = 75 and 5 * 15 = 75

This is a proportion because the cross products are equal.

Option D: 4, 3, 36, 18

Checking the cross product:

4 * 18 = 72 and 3 * 36 = 108

This is a proportion because the cross products are equal.

The correct answer is C: 3, 5, 15, 25 because the cross products are equal.

To simplify the ratio 144:28, we need to find the greatest common divisor (GCD) of 144 and 28 and divide both numbers by this GCD.

First, let's find the factors of each number:

• The factors of 144 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
• The factors of 28 are: 1, 2, 4, 7, 14, and 28.

The greatest common divisor (GCD) of 144 and 28 is 4.

Now, divide both 144 and 28 by 4:

144 ÷ 4 = 36

28 ÷ 4 = 7

So, the simplified ratio is 36:7.

The correct answer is B: 36:7.

- The problem involves finding the mean proportion between two pairs of numbers in a proportion: 25:10 and 10:4.
- In a proportion (a:b::c:d), the mean proportion or geometric mean is the middle term (b) when (a:b = b:c).
- Here, the numbers 25, 10, 10, and 4 form the proportion (25:10::10:4).
- The mean proportion is 10, as it is the common term between the two ratios.

The proportion given is x : y = y : z. This can be written as:

x / y = y / z

Now, we cross-multiply:

y * y = x * z

This simplifies to:

y² = xz

The correct answer is B: y² = xz.

For the numbers to be in proportion, the following condition must hold:

a / b = b / c

Where a, b, and c are the three numbers. The given numbers are ___, 32, and 64. Let’s denote the missing number as a.

So, the proportion is:

a / 32 = 32 / 64

Simplify the right-hand side:

32 / 64 = 1 / 2

Now, we have the equation:

a / 32 = 1 / 2

By cross-multiplying:

a * 2 = 32 * 1

This simplifies to:

2a = 32

Solving for a:

a = 32 / 2 = 16

The missing number is 16, so the correct answer is C: 16.

To check if the ratios are in proportion, we compare the two ratios as follows:

The first ratio is 6 : 3, which simplifies to:

6 / 3 = 2

The second ratio is 5 : 15, which simplifies to:

5 / 15 = 1 / 3

Since the simplified values are 2 and 1/3, these two ratios are not equal. Therefore, the given ratios 6:3 and 5:15 are not in proportion.

So, the correct answer is A: The given ratios are not in proportion.

The given proportion is:

5 : 120 :: 40 : x

This can be written as:

5 / 120 = 40 / x

Now, cross-multiply to solve for x:

5 × x = 120 × 40

5x = 4800

Now, divide both sides by 5 to find x:

x = 4800 / 5 = 960

Thus, the fourth term is 960.

So, the correct answer is C: 960.

The given proportion is:

6 : ? :: 12 : 36

This can be written as:

6 / x = 12 / 36

Now, simplify 12 / 36:

12 / 36 = 1 / 3

Now, cross-multiply:

6 * 3 = x * 1

18 = x

Thus, the second term is 18.

The correct answer is B: 18.

Ratio of number of boys to number of girls = 2 : 3
Number of girls = 180
Let the number of boys be x.
⇒ 2/3 = x/180 [∵ they are equivalent ratios]
⇒ 3x = 2×180
⇒ x = 360/3
⇒ x = 120
∴ Number of boys are 120.

Given the ratio of lemons to cups of water is 3 : 5, we need to find the number of cups of water required for 12 lemons.

Let the number of cups of water be x.

From the given ratio:

Lemons : Cups of water = 3 : 5

We can set up the proportion:

12 / x = 3 / 5

Now, cross-multiply to solve for x:

5 * 12 = 3 * x

60 = 3x

x = 60 / 3 = 20

Therefore, the number of cups of water required is 20.

Correct Answer: C: 20

In a cricket team, there are 11 players in total. Out of these, generally, only one player is designated as the wicketkeeper.

The ratio of the total number of players (11) to the number of wicketkeepers (1) is:

Ratio = 11 : 1

Correct answer: B: 11 : 1

The word GEOMETRY contains the following vowels and consonants:

• Vowels: E, O, E (3 vowels)
• Consonants: G, M, T, R, Y (5 consonants)

So, the ratio of consonants to vowels is:

5 consonants : 3 vowels

Correct answer: B: 5 : 3