Test: Ratio, Proportion and Unitary Method - Class 7 MCQ

To simplify the ratio 48:36, find the greatest common divisor (GCD) which is 12. Dividing both terms by 12 gives 48 ÷ 12 = 4 and 36 ÷ 12 = 3. Thus, the simplest form is 4:3. This means that for every 4 parts of one quantity, there are 3 parts of the other.

The total work done is constant. If 6 workers take 12 days, the total work is 6 workers × 12 days = 72 worker-days. If 8 workers are working, the number of days required is 72 worker-days ÷ 8 workers = 9 days. This demonstrates the principle of inverse variation where increasing the number of workers decreases the time taken.

The relationship is inversely proportional. If 5 workers take 10 days, the total work done is 5 × 10 = 50 worker-days. If 10 workers are used, then the time taken is 50 worker-days ÷ 10 workers = 5 days.

The ratio of flour to sugar is 2:3. If you have 10 cups of flour, use the ratio to find sugar. Set up the proportion: 2/3 = 10/x. Cross-multiplying gives 2x = 30, so x = 15. Therefore, you need 15 cups of sugar.

The ratio of milk to water is 3:1. If there are 12 liters of milk, we can set up the ratio as 3x = 12. Solving for x gives x = 4, which means there are 4 liters of water in the mixture. This ratio illustrates how components can be proportionally mixed.

The ratio of red balls to blue balls is 10:15. To simplify, divide by the GCD, which is 5. This results in 10 ÷ 5 = 2 and 15 ÷ 5 = 3, yielding a simplest form of 2:3.

To find the equivalent ratio, multiply both terms of the ratio 5:7 by 3. This results in 5 × 3 = 15 and 7 × 3 = 21, giving the equivalent ratio of 15:21. Equivalent ratios maintain the same relationship between the quantities.

Increasing both terms of the ratio 7:9 by 2 gives 7 + 2 = 9 and 9 + 2 = 11, resulting in the new ratio of 9:11. This demonstrates how altering both terms affects the overall relationship.

The ratio of boys to girls is 3:5. If there are 15 boys, we can set up the proportion 3/5 = 15/x. Cross-multiplying gives 3x = 75. Dividing by 3, x = 25. Therefore, there are 25 girls in the class.

First, find the cost of one pen: $8 ÷ 4 pens = $2 per pen. To find the cost of 10 pens, multiply $2 by 10, resulting in $20. This method of finding the value of one unit before calculating the total is known as the unitary method.

Direct variation describes a relationship where an increase in one quantity results in an increase in another. In this case, as the temperature rises, the rate of ice melting also increases, demonstrating a direct relationship.

To find the compound ratio of 3:4 and 2:5, multiply the antecedents (3 * 2) for the new antecedent and the consequents (4 * 5) for the new consequent. This gives 6:20, which can be simplified to 3:10. Compound ratios are formed by combining ratios through multiplication.

The ratio 1:3 consists of 1 part + 3 parts, which totals 4 parts. Ratios indicate the proportional parts of the whole, and in this case, they represent 4 equal divisions of a quantity.

Set up the proportion 3/4 = x/36. Cross-multiplying gives 4x = 108. Dividing by 4 gives x = 27. Therefore, there are 27 boys in the class, reflecting the maintained ratio of boys to girls.

Let the ages be represented by 4x (younger) and 5x (elder). Given that the younger brother is 12, we can set 4x = 12. Solving for x gives x = 3. Therefore, the elder brother’s age is 5x = 5 * 3 = 15 years old.

For ratios to be compared accurately, the quantities involved must be in the same unit. This ensures that the comparison is valid. For example, comparing 5 kg of apples to 10 kg of oranges is valid, but comparing 5 kg of apples to 10 liters of milk is not.

A continued ratio combines three quantities where the middle term is the same, thus 8:12 and 12:15 gives the continued ratio of 8:12:15. This format helps in comparing three related quantities directly.

To simplify the ratio 30:50, find the GCD, which is 10. Dividing both terms gives 30 ÷ 10 = 3 and 50 ÷ 10 = 5, resulting in the simplest form of 3:5. This indicates that for every 3 meters of one quantity, there are 5 meters of the other.

The distance to time ratio is 120 km to 2 hours, which simplifies to 120:2. Dividing both sides by 2 results in the ratio of 60:1, indicating that for every 1 hour, the car travels 60 km.

Using the ratio of 2:5, if the smaller rectangle's length is represented by 2x and equals 10 cm, then 2x = 10, giving x = 5. The length of the larger rectangle is 5x = 5 * 5 = 25 cm.