This worksheet is about
Indirect Proportion (also called Inverse Proportion). In indirect proportion, when one quantity increases, the other decreases, and vice versa —
as long as their product remains constant.
The general formula for indirect proportion is:
>
Number of workers × Time = Constant
Or more generally:
>
A × B = k (where k is constant)
So if A increases, B must decrease to keep the product the same.
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Let’s solve each question step by step.
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1) 4 people can paint a fence in 3 hours. How long will it take 6 people to paint it?
We assume the total “work” is constant.
Total work = People × Time = 4 × 3 =
12 person-hours
Now, with 6 people:
Time = Total work ÷ Number of people = 12 ÷ 6 =
2 hours
✔ Answer: 2 hours
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2) 12 workers build a wall in 10 hours. How long do 5 workers build a wall?
Total work = 12 × 10 =
120 worker-hours
With 5 workers:
Time = 120 ÷ 5 =
24 hours
✔ Answer: 24 hours
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3) 3 pipes take 60 minutes to water the field. How much time will it take to water the field with 6 pipes?
Total “pipe-minutes” = 3 × 60 =
180 pipe-minutes
With 6 pipes:
Time = 180 ÷ 6 =
30 minutes
✔ Answer: 30 minutes
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4) 8 men can do a certain job in 12 days. How many men will be required to do the same job in 16 days?
Total work = 8 × 12 =
96 man-days
To finish in 16 days:
Men needed = 96 ÷ 16 =
6 men
✔ Answer: 6 men
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5) A contractor hired 150 men to pave a road in 30 days. How many men will he hire to do the same work in 20 days?
Total work = 150 × 30 =
4500 man-days
To finish in 20 days:
Men needed = 4500 ÷ 20 =
225 men
✔ Answer: 225 men
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6) 12 men can dig a pond in 8 days. How many men can dig it in 6 days?
Total work = 12 × 8 =
96 man-days
To finish in 6 days:
Men needed = 96 ÷ 6 =
16 men
✔ Answer: 16 men
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7) 15 workers can build a wall in 48 hours. How many workers will be required to do the same work in 30 hours?
Total work = 15 × 48 =
720 worker-hours
To finish in 30 hours:
Workers needed = 720 ÷ 30 =
24 workers
✔ Answer: 24 workers
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##
✔ Final Answers:
1)
2 hours
2)
24 hours
3)
30 minutes
4)
6 men
5)
225 men
6)
16 men
7)
24 workers
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## 💡 Key Concept Recap:
In indirect proportion problems like these,
more workers = less time, and
fewer workers = more time. The product (workers × time) stays constant for the same amount of work.
You can always set up:
Initial workers × Initial time = New workers × New time
Then solve for the unknown.
Let me know if you want diagrams or tables to visualize this!
Parent Tip: Review the logic above to help your child master the concept of inverse proportion worksheet.
