Class 8 Maths worksheet focusing on inverse proportion with various word problems and spaces for answers.

Worksheet: Direct and Inverse Proportions

#### Topic: Inverse Proportion

Let's solve each problem step by step.

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1. The number of \( x \) men hired to construct a wall and the time \( y \) taken to finish the job.

- Explanation: If more men are hired, the time taken to complete the job decreases. This is an example of inverse proportion.
- Answer: Inverse Proportion

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2. The length \( x \) of a journey by bus and price \( y \) of the ticket.

- Explanation: Generally, the longer the journey, the higher the price of the ticket. This is an example of direct proportion.
- Answer: Direct Proportion

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3. Journey ( \( x \) km) undertaken by a car and the petrol ( \( y \) litres) consumed by it.

- Explanation: The more distance traveled, the more petrol is consumed. This is an example of direct proportion.
- Answer: Direct Proportion

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4. If 36 men can do a piece of work in 25 days, in how many days will 15 men do it?

- Explanation: This is an inverse proportion problem because fewer men will take more days to complete the same work.
- Formula: \( \text{Men} \times \text{Days} = \text{Constant} \)
- Given: \( 36 \times 25 = 900 \) (constant)
- To find: Days taken by 15 men
\[
15 \times \text{Days} = 900 \implies \text{Days} = \frac{900}{15} = 60
\]
- Answer: 60 days

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5. A work force of 50 men with a contractor can finish a piece of work in 5 months. In how many months the same work can be completed by 125 men?

- Explanation: This is an inverse proportion problem because more men will take fewer months to complete the same work.
- Formula: \( \text{Men} \times \text{Months} = \text{Constant} \)
- Given: \( 50 \times 5 = 250 \) (constant)
- To find: Months taken by 125 men
\[
125 \times \text{Months} = 250 \implies \text{Months} = \frac{250}{125} = 2
\]
- Answer: 2 months

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6. A work-force of 420 men with a contractor can finish a certain piece of work in 9 months. How many extra men must he employ to complete the job in 7 months?

- Explanation: This is an inverse proportion problem because more men will take fewer months to complete the same work.
- Formula: \( \text{Men} \times \text{Months} = \text{Constant} \)
- Given: \( 420 \times 9 = 3780 \) (constant)
- To find: Number of men required to complete the work in 7 months
\[
\text{Men} \times 7 = 3780 \implies \text{Men} = \frac{3780}{7} = 540
\]
- Extra men required: \( 540 - 420 = 120 \)
- Answer: 120 extra men

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7. 1200 men can finish a stock of food in 35 days. How many more men should join them so that the same stock may last for 25 days?

- Explanation: This is an inverse proportion problem because more men will consume the food faster, reducing the number of days it lasts.
- Formula: \( \text{Men} \times \text{Days} = \text{Constant} \)
- Given: \( 1200 \times 35 = 42000 \) (constant)
- To find: Number of men required for the food to last 25 days
\[
\text{Men} \times 25 = 42000 \implies \text{Men} = \frac{42000}{25} = 1680
\]
- Extra men required: \( 1680 - 1200 = 480 \)
- Answer: 480 extra men

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8. In a hostel of 50 girls, there are food provisions for 40 days. If 30 more girls join the hostel, how long will these provisions last?

- Explanation: This is an inverse proportion problem because more girls will consume the food faster, reducing the number of days it lasts.
- Formula: \( \text{Girls} \times \text{Days} = \text{Constant} \)
- Given: \( 50 \times 40 = 2000 \) (constant)
- Total girls after 30 join: \( 50 + 30 = 80 \)
- To find: Number of days the provisions will last for 80 girls
\[
80 \times \text{Days} = 2000 \implies \text{Days} = \frac{2000}{80} = 25
\]
- Answer: 25 days

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9. 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?

- Explanation: This is an inverse proportion problem because more cows will graze the field faster, reducing the number of days it lasts.
- Formula: \( \text{Cows} \times \text{Days} = \text{Constant} \)
- Given: \( 55 \times 16 = 880 \) (constant)
- To find: Number of cows required to graze the field in 10 days
\[
\text{Cows} \times 10 = 880 \implies \text{Cows} = \frac{880}{10} = 88
\]
- Answer: 88 cows

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10. 18 men can reap a field in 35 days. For reaping the same field in 15 days, how many men are required?

- Explanation: This is an inverse proportion problem because more men will reap the field faster, reducing the number of days it takes.
- Formula: \( \text{Men} \times \text{Days} = \text{Constant} \)
- Given: \( 18 \times 35 = 630 \) (constant)
- To find: Number of men required to reap the field in 15 days
\[
\text{Men} \times 15 = 630 \implies \text{Men} = \frac{630}{15} = 42
\]
- Answer: 42 men

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Final Answers:

1. Inverse Proportion
2. Direct Proportion
3. Direct Proportion
4. 60 days
5. 2 months
6. 120 extra men
7. 480 extra men
8. 25 days
9. 88 cows
10. 42 men

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{Inverse Proportion} \\
2. \text{Direct Proportion} \\
3. \text{Direct Proportion} \\
4. 60 \text{ days} \\
5. 2 \text{ months} \\
6. 120 \text{ extra men} \\
7. 480 \text{ extra men} \\
8. 25 \text{ days} \\
9. 88 \text{ cows} \\
10. 42 \text{ men}
\end{array}
}
\]