Class 8 Maths Chapter 11 Practice Question Answers - Direct and Inverse Proportions

Q1: If 15 workers can finish a task in 42 hours, calculate the number of workers required to complete the same task in 30 hours.
Sol:
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.

Q2: If the cost of 20 pens is Rs. 180, calculate the cost of 15 pens?
Sol:
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.

Q3: If the increase in time causes a corresponding decrease in the price of a product. Identify the proportionality.
Sol:
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.

Q4: Identify the variation: “For the increase in speed, the time to cover a fixed distance reduces”.
Sol:
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.

Q5: 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?
Sol:
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.

Q6: If a horse eats 18 kg of com in 12 days ? What is the quantity it eats in 9 days ?
(a) 12.5 kg
(b) 11.5 kg
(c) 12.5 kg
(d) 13.5 kg
Ans: (d)
Sol: The rate at which the horse is eating corn can be calculated as:
Rate = Quantity / Time
Given that the horse eats 18 kg of corn in 12 days, the rate is:
Rate = 18 kg / 12 days = 1.5 kg/day
Now, to find the quantity the horse eats in 9 days, we can use the rate:
Quantity = Rate × Time
Quantity = 1.5 kg/day × 9 days
Quantity = 13.5 kg
So, the horse eats 13.5 kg of corn in 9 days.
Therefore, the correct answer is: (d) 13.5 kg

Q7: If a boy can run 1 km in 10 minutes. How long will he take to run 600 m?
(a) 4 minutes
(b) 2 minutes
(c) 3 minutes
(d) 6 minutes
Ans: (d)
Sol: Given that the boy can run 1 km in 10 minutes, we can use this information to calculate the time it will take him to run 600 m.
The ratio of distance to time for the two runs will be the same:
1 km / 10 minutes = 600 m / x
Where x is the time it will take to run 600 m.
Solving for x:
x = (600 m × 10 minutes) / 1 km
x = 6000 m · minutes / 1000 m
x = 6 minutes
So, the boy will take 6 minutes to run 600 m.
Therefore, the correct answer is: (d) 6 minutes

Q8: If 8 g of sandal wood cost Rs 40, what is the cost of 10 g ?
(a) Rs 50
(b) Rs 36
(c) Rs 48
(d) Rs 30
Ans: (a)
Sol: Given that 8 g of sandalwood cost Rs 40, we can find the cost of 10 g using proportion.
Let's set up a proportion:
Cost of 8 g / Weight of 8 g = Cost of 10 g / Weight of 10 g
40 / 8 = Cost of 10 g / 10
Solving for the cost of 10 g:
Cost of 10 g = (40 / 8) × 10
Cost of 10 g = 5 × 10
Cost of 10 g = Rs 50
So, the cost of 10 g of sandalwood is Rs 50.
Therefore, the correct answer is: (a) Rs 50

Q9: 3 lambs finish eating turnips in 8 days. How many days will it take for 2 lambs to finish them?
(a) 8
(b) 6
(c) 12
(d) 10
Ans: (a)
Sol: Let's use the concept of "work done" to solve this problem. If 3 lambs can finish eating turnips in 8 days, then the work done by those 3 lambs in 1 day is equal to the amount of turnips they eat in 1 day.
Let "W" be the amount of turnips that 3 lambs eat in 1 day.
Now, 2 lambs will eat turnips at a different rate, but the total work remains the same (the turnips are still getting eaten). Let "D" be the number of days it takes for 2 lambs to finish eating the turnips.
So, the work done by 2 lambs in D days is 2 times the amount of turnips they eat in 1 day, which is 2W.
Since the total work remains the same:
3 lambs' work in 1 day = 2 lambs' work in D days
W = 2W × D
Solving for D:
D = 1 / 2
D = 0.5 days
Since it's not possible for lambs to eat for half a day, we need to choose the next whole number of days, which is 1 day.
Therefore, the correct answer is: (a) 8