All questions of Ratio for Grade 6 Exam

Given: x, 30, 24, 16 are in proportion.

To find: The value of x.

Solution:

The given numbers are in proportion. This means that the ratio of any two consecutive numbers is equal to the ratio of the other two consecutive numbers.

Therefore, we can write:

x/30 = 24/16

Cross-multiplying, we get:

16x = 30 × 24

Simplifying, we get:

16x = 720

Dividing both sides by 16, we get:

x = 45

Therefore, the value of x is 45.

Hence, option A is the correct answer.

Given ratio is 3:8.

To obtain the new ratio, we need to add 4 to the antecedent and 2 to the consequent.

Adding 4 to the antecedent of 3, we get 7.
Adding 2 to the consequent of 8, we get 10.

Therefore, the new ratio is 7:10.

Hence, the correct answer is option D.

Answer is c here

18/16 = 9/8


99/88 = 9/8


9/8 : 9/8


, That is why A (88) is correct

Correct answer is option A

To solve this proportion, we need to determine the relationship between the first pair of numbers and apply the same relationship to the second pair of numbers.

In the given proportion, 9:3 and 36:12, we can see that both pairs have a ratio of 3:1. This means that for every 3 in the first pair, there is 1 in the second pair.

To find the extremes of the proportion, we need to identify the first and last numbers in each pair. In the first pair, the first number is 9 and the last number is 3. In the second pair, the first number is 36 and the last number is 12.

Therefore, the extremes of the proportion are 9 and 12.

Hence, the correct answer is option D) 9, 12.

Understanding Proportions
When we say that four quantities are in proportion, it means that the ratio of the first two quantities is equal to the ratio of the last two quantities. Here, we have:
- x : 24 = 30 : 16
This can be expressed as:
- x / 24 = 30 / 16
Cross-Multiplication
To solve for x, we can use cross-multiplication:
- x * 16 = 30 * 24
Calculating the Right Side
Now, let's calculate 30 * 24:
- 30 * 24 = 720
So, we have:
- x * 16 = 720
Isolating x
Next, we need to isolate x by dividing both sides by 16:
- x = 720 / 16
Performing the Division
Now, let's perform the division:
- 720 ÷ 16 = 45
Thus, we find:
- x = 45
Conclusion
Therefore, the value of x is 45, confirming that the correct answer is option 'B'.
- x = 45 means that the ratios are consistent and maintain the same proportional relationship.
This demonstrates a fundamental concept in mathematics about ratios and proportions, essential in various real-life applications.

2÷210=140

4

6

Answer will be 5:4

Ratio refers to the quantitative relationship between two amounts or values. It is expressed in the form of a:b, where a and b are the two values being compared.

To find the ratio of 81 to 108, we need to divide both numbers by their greatest common factor, which is 27.

81 ÷ 27 = 3
108 ÷ 27 = 4

Therefore, the ratio of 81 to 108 is 3:4.

Option C, "it is 3:4", is the correct answer.

To find the ratio of length to breadth, we need to divide the length of the room by the breadth of the room.

Given:
Length of the room = 30 m
Breadth of the room = 20 m

To find the ratio of length to breadth, we divide the length by the breadth:

Ratio = Length / Breadth

Let's calculate:

Ratio = 30 m / 20 m

Simplifying the division, we get:

Ratio = 3/2

Thus, the ratio of length to breadth is 3:2, which corresponds to option B.

Explanation:
The ratio of length to breadth represents the relationship between the length and breadth of the room. In this case, the length is 30 m and the breadth is 20 m. When we divide the length by the breadth, we get a ratio of 3/2. This means that for every 3 units of length, there are 2 units of breadth. So, the ratio of length to breadth is 3:2.

In a cricket team, the ratio of the total number of players to the number of wicket keepers is 11:1. This means that for every 11 players in the team, there is only 1 wicket keeper. Let's understand this in more detail.

Understanding the Roles in a Cricket Team:
Cricket is a team sport played between two teams, with each team consisting of multiple players. In a cricket team, there are various roles and positions that players take up. One of the important positions is that of a wicket keeper.

What is a Wicket Keeper?
A wicket keeper is a player who stands behind the stumps (the set of three wooden sticks called wickets) to catch the ball and try to dismiss the batsman. The wicket keeper plays a crucial role in the team as they are responsible for catching the ball when the batsman misses it or edges it.

The Ratio of Players to Wicket Keepers:
In a cricket team, there are typically 11 players on the field at any given time. These players can have various roles such as batsmen, bowlers, and fielders. However, there is only one wicket keeper who stands behind the stumps.

Therefore, the ratio of the total number of players to the number of wicket keepers is 11:1. This means that for every 11 players in the team, there is only 1 wicket keeper.

Example:
Let's consider an example to illustrate this. Suppose we have a cricket team with a total of 22 players. In this case, the ratio of the total number of players to the number of wicket keepers would be 22:2, which can be simplified to 11:1. This means that in a team of 22 players, there would be 2 wicket keepers.

Conclusion:
In summary, the ratio of the total number of players to the number of wicket keepers in a cricket team is 11:1. This ratio implies that for every 11 players, there is only 1 wicket keeper. It is important to have a wicket keeper in the team as they play a crucial role in catching the ball and trying to dismiss the batsman.

Ratios:
A ratio is a comparison of two quantities. It is expressed in the form of a fraction or using a colon (:). For example, if we have two quantities A and B, the ratio of A to B can be written as A/B or A:B.

Equality of Ratios:
Two ratios are said to be equal if they represent the same comparison between quantities. In other words, the two ratios have the same value.

Conditions for Ratios to be Equal:
To determine if two ratios are equal, we can use different methods. However, the most common condition for two ratios to be equal is when the product of the means is equal to the product of the extremes.

Explanation:
Let's consider two ratios, A/B and C/D. According to the condition for equality of ratios, we have the following equation:

(A/B) = (C/D)

To check if the condition holds true, we can cross multiply the terms:

A * D = B * C

If the product of the means (B * C) is equal to the product of the extremes (A * D), then the two ratios are equal.

Example:
Let's take an example to understand this concept better. Consider the ratios 2/3 and 4/6. We can check if they are equal using the condition mentioned above:

Product of means = (3 * 4) = 12
Product of extremes = (2 * 6) = 12

Since the product of the means is equal to the product of the extremes (12 = 12), the two ratios are equal.

Conclusion:
In summary, two ratios are equal if the product of the means is equal to the product of the extremes. This condition allows us to determine if two ratios represent the same comparison between quantities.

Ratio

Option 1:2