Some important class 8 maths questions for chapter 13 direct and inverse proportions are given here to help the students to get acquainted with different variations of questions and thus, score well in the class 9 CBSE exam. These direct and inverse proportion questions include many long answer type, short answer type and HOTS questions which will also encourage students to develop their problem-solving skills.
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Direct and Inverse Proportions Questions For Class 8 (Chapter 13)
A few important direct and inverse questions with solutions for class 8 are given below. There are many additional practice questions that students can practice once they are thoroughly introduced with the concepts.
Important Direct and Inverse Proportion Questions (With Solutions)
1. If the increase in time causes a corresponding decrease in the price of a product. Identify the proportionality.
As per the given question, the increase in time reduces the price of a product. Thus,
Time ∝ 1/Product Price
Hence, the time and price of the product are inversely proportional.
2. Identify the variation: “For the increase in speed, the time to cover a fixed distance reduces”.
In this case, an increase in speed results in a decrease in time. So,
Speed ∝ 1/Time
So, this relation is a case of indirect variation.
3. If the cost of 20 pens is Rs. 180, calculate the cost of 15 pens?
Given that 20 pens cost Rs. 180.
Now, let the cost of 15 pens be Rs. x
In such a condition, the cost of pens changes directly with the total number of pens i.e. they are directly proportional.
20/180 = 15/x
Or, x = Rs. 135.
4. A car travels 14km in 25 minutes. Find out how far the car can travel in 5 hours if the speed remains the same?
It is given that the car travels 14km in 25 minutes.
Now, assume that the distance the car can travel in 5 hours be x.
Since 1 hour = 60 minutes, 5 hours = 300 minutes.
Thus, the two given statements are
14km —————–> 25 minutes
And, x km —————–> 300 minutes
We know that the distance travelled by car and the time taken by the car is directly proportional to each other.
14/25 = x/300
=> x = 168 km.
5. If 15 workers can finish a task in 42 hours, calculate the number of workers required to complete the same task in 30 hours?
In this situation, the number of workers varies directly with the time required to finish a task.
Thus, they are inversely proportional.
Now, assume that the number of workers required to complete the task in 30 hours be “x”.
Here, the number of workers ∝ 1/hours
Number of workers = C/hours (here “C” is the constant of proportionality)
Now, consider the first case: “15 workers can finish a task in 42 hours”
Here, 15 = C/42
=> C = 15 × 42 = 630.
Now, consider the second case: “x workers can finish a task in 30 hours”
Here, x = C/30
=> x = 630/30
Or, x = 21
So, the number of 21 workers are required to complete the task in 30 hours.