Direct or Indirect Proportion worksheet - Free Printable

Let's analyze each of the 10 problems to determine whether they involve direct proportion (D) or inverse proportion (I). We'll go step by step, explain the reasoning, and then give the correct answer.

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1. If the total daily wages of 7 women or 5 men is $525. What will be the daily wage of 13 and 7 women and men respectively?

- Analysis:
The total daily wage for 7 women = $525 → so one woman earns $525/7 = $75.
Similarly, 5 men earn $525 → one man earns $525/5 = $105.
Now, we're asked to find the daily wage of 13 men and 7 women — this is just multiplication:
- 13 men: 13 × $105 = $1365
- 7 women: 7 × $75 = $525

This is a direct proportion because more people → higher total wage (proportional).

✔ Answer: D

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2. The cost of 16 bars of soap each weighing 1.5 kg is $672. Calculate the cost of 18 similar bars of soap each weighing 2 kg.

- Analysis:
Cost depends on both number of bars and weight per bar.
- More bars → higher cost (direct)
- Heavier bars → higher cost (direct)
So overall, cost is directly proportional to both number and weight.
This is a compound direct proportion.

✔ Answer: D

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3. If 32 men can reap a field in 15 days, in how many days can 20 men reap the same field?

- Analysis:
More men → less time needed → inverse relationship between number of men and days.
This is inverse proportion.

✔ Answer: I

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4. The fuel consumption of a vehicle is 6.8L/102km. What distance can this vehicle cover in 24 liters of fuel?

- Analysis:
Fuel used ∝ Distance covered (more fuel → more distance).
This is direct proportion.

✔ Answer: D

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5. The cost of ferrying 160 bags of cement for 125 km is Rs. 60. What will be the cost of ferrying 200 bags for 400 km?

- Analysis:
Cost increases with:
- More bags → more cost (direct)
- Longer distance → more cost (direct)
So it’s a direct proportion with two variables.

✔ Answer: D

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6. The wages for 12 men working for 5 days are $7500. Calculate the wages of 17 men working for 6 days.

- Analysis:
Wages increase with:
- More men → more wages (direct)
- More days → more wages (direct)
So, wages are directly proportional to both number of men and number of days.

✔ Answer: D

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7. 12 men can dig a pond in 8 days. How many men can dig it in 6 days?

- Analysis:
Fewer days → need more men → inverse relationship between number of men and time.
So this is inverse proportion.

✔ Answer: I

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8. A hostel has enough food for 125 students for 16 days. How long will the food last if 75 more students join them?

- Analysis:
More students → food lasts fewer days → inverse relationship between number of students and duration.
So this is inverse proportion.

✔ Answer: I

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9. A fort had enough food for 80 soldiers for 60 days. How long would the food last if 20 more soldiers join after 15 days?

- Analysis:
After 15 days, some food is consumed. Then 100 soldiers (80 + 20) consume the remaining food.
The food consumption rate changes with more soldiers → more soldiers → shorter time.
So the remaining time is inversely proportional to number of soldiers.
This involves inverse proportion.

✔ Answer: I

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10. 500 soldiers in a fort had enough food for 30 days. After 6 days, some soldiers were sent to another fort and thus the food lasted for 32 more days. How many soldiers left the fort?

- Analysis:
After 6 days, food for 500 soldiers lasts 24 days (since 30–6=24).
But now it lasts 32 more days → fewer soldiers → food lasts longer → inverse proportion between number of soldiers and number of days.

✔ Answer: I

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | D |
| 2 | D |
| 3 | I |
| 4 | D |
| 5 | D |
| 6 | D |
| 7 | I |
| 8 | I |
| 9 | I |
| 10 | I |

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🔍 Summary of Rules:

- Direct Proportion (D): When one quantity increases, the other also increases proportionally.
- e.g., more workers → more work done (in fixed time), more fuel → more distance.
- Inverse Proportion (I): When one increases, the other decreases.
- e.g., more workers → less time to complete work, more people → food lasts fewer days.

Let me know if you'd like the actual calculations for any of these!