Class 8 Maths Chapter 11 HOTS Questions - Direct and Inverse Proportions

Q1: If the increase in time causes a corresponding decrease in the price of a product. Identify the proportionality.
Ans: 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.

Q2: Identify the variation: “For the increase in speed, the time to cover a fixed distance reduces”.
Ans: 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.

Q3: If the cost of 20 pens is Rs. 180, calculate the cost of 15 pens?
Ans: 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.
So,
20/180 = 15/x
Or, x = Rs. 135.

Q4: A car travels 14 km in 25 minutes. Find out how far the car can travel in 5 hours if the speed remains the same?
Ans: It is given that the car travels 14 km 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
14 km —————–> 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.
So,
14/25 = x/300
⇒ x = 168 km.

Q5: If 15 workers can finish a task in 42 hours, calculate the number of workers required to complete the same task in 30 hours.
Ans: In this situation, the number of workers varies indirectly 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
Or,
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.