Let's solve each of these
indirect proportion problems step by step.
>
Indirect Proportion (Inverse Proportion):
When one quantity increases, the other decreases in such a way that their product remains constant.
For example:
- More workers → Less time to complete work
- More pipes → Less time to water the field
We use the formula:
$$
\text{Work} = \text{Number of people} \times \text{Time}
$$
So,
$$
P_1 \times T_1 = P_2 \times T_2
$$
where $P$ is number of people/pipes/workers and $T$ is time.
---
1) 4 people can paint a fence in 3 hours. How long will it take 6 people to paint it?
Let $T$ be the time for 6 people.
Using indirect proportion:
$$
4 \times 3 = 6 \times T \\
12 = 6T \\
T = \frac{12}{6} = 2 \text{ hours}
$$
✔ Answer: 2 hours
---
2) 12 workers build a wall in 10 hours. How long do 5 workers build a wall?
Let $T$ be the time for 5 workers.
$$
12 \times 10 = 5 \times T \\
120 = 5T \\
T = \frac{120}{5} = 24 \text{ hours}
$$
✔ Answer: 24 hours
---
3) 3 pipes take 60 minutes to water the field. How much time will it take with 6 pipes?
$$
3 \times 60 = 6 \times T \\
180 = 6T \\
T = \frac{180}{6} = 30 \text{ minutes}
$$
✔ Answer: 30 minutes
---
4) 8 men can do a job in 12 days. How many men are required to do the same job in 16 days?
Let $M$ be the number of men needed.
$$
8 \times 12 = M \times 16 \\
96 = 16M \\
M = \frac{96}{16} = 6
$$
✔ Answer: 6 men
---
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?
Let $M$ be the number of men needed.
$$
150 \times 30 = M \times 20 \\
4500 = 20M \\
M = \frac{4500}{20} = 225
$$
✔ Answer: 225 men
---
6) 12 men can dig a pond in 8 days. How many men can dig it in 6 days?
Let $M$ be the number of men.
$$
12 \times 8 = M \times 6 \\
96 = 6M \\
M = \frac{96}{6} = 16
$$
✔ Answer: 16 men
---
7) 15 workers can build a wall in 48 hours. How many workers are required to do the same work in 30 hours?
Let $W$ be the number of workers.
$$
15 \times 48 = W \times 30 \\
720 = 30W \\
W = \frac{720}{30} = 24
$$
✔ Answer: 24 workers
---
✔ Final Answers Summary:
1)
2 hours
2)
24 hours
3)
30 minutes
4)
6 men
5)
225 men
6)
16 men
7)
24 workers
These are all examples of
inverse proportion, where increasing the number of workers reduces the time taken, and vice versa. The total work done (in man-hours or worker-days) stays constant.
Parent Tip: Review the logic above to help your child master the concept of word problems proportions worksheet.
