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 wage for 7 women = $525 → so one woman earns $525/7 = $75/day.
Similarly, 5 men earn $525 → one man earns $525/5 = $105/day.
Now we can find wages for 13 men and 7 women:
- 13 men: 13 × $105 = $1365
- 7 women: 7 × $75 = $525

But the key here is: The number of people and total wage are directly proportional — more people → higher total wage (if rate is constant). So this is a direct proportion.

✔ 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 number of bars and weight per bar. Both increase:
- More bars → more cost (direct)
- Heavier bars → more cost (direct)

So total cost is directly proportional to both number and weight → overall 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 to complete work → inverse relationship between number of men and time taken.

This is a classic inverse proportion:
Men × Days = Constant (work done)

✔ 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 consumed ∝ 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 (direct)
- Longer distance (direct)

So cost is directly proportional to both number of bags and distance → overall direct proportion.

✔ 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 depend on:
- Number of men (more men → more wages) → direct
- Number of days (more days → more wages) → direct

So total wages ∝ number of men × number of days → direct proportion.

✔ 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:
More men → fewer days needed → inverse relationship between 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.

Total food = number of students × days → constant

✔ 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:
This is a two-part situation. First, food lasts 15 days for 80 soldiers. Then, after that, 100 soldiers consume the remaining food.
The number of soldiers affects how long food lasts → 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:
Initially, 500 soldiers eat for 6 days → food consumed = 500 × 6 = 3000 soldier-days.
Remaining food = 500 × 24 = 12,000 soldier-days.
Let x soldiers remain → they eat for 32 days → x × 32 = 12,000 → x = 375
So 500 – 375 = 125 soldiers left.

The number of soldiers and time the food lasts are inversely related → inverse proportion.

✔ 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:

- Direct Proportion (D): When one quantity increases, the other increases proportionally.
- Examples: More workers → more wages; more fuel → more distance; more bags → more cost.

- Inverse Proportion (I): When one quantity increases, the other decreases proportionally.
- Examples: More workers → less time to finish work; more people → food lasts fewer days.

Let me know if you'd like full calculations for any problem!