Direct and Inverse Proportions (Inverse Proportion) worksheet ... - Free Printable

Let's solve each question from the Class 8 Maths Worksheet on Direct and Inverse Proportions, focusing on Inverse Proportion.

---

Understanding Direct and Inverse Proportion:

- Direct Proportion: As one quantity increases, the other also increases at a constant rate.
Example: More men → more work done in same time.

- Inverse Proportion: As one quantity increases, the other decreases.
Example: More men → less time to complete the job.

We use:
- For inverse proportion: $ x_1 \times y_1 = x_2 \times y_2 $
- For direct proportion: $ \frac{x_1}{y_1} = \frac{x_2}{y_2} $

---

Solutions:

#### 1. The number of x men hired to construct a wall and the time y taken to finish the job.
- More men → Less time (inverse)
✔ Answer: Inversely

#### 2. The length x of a journey by bus and price y of the ticket.
- Longer journey → Higher price (direct)
✔ Answer: Directly

#### 3. Journey (x km) undertaken by a car and the petrol (y litres) consumed by it.
- More distance → More petrol used (direct)
✔ Answer: Directly

#### 4. If 36 men can do a piece of work in 25 days, in how many days will 15 men do it?
- This is inverse proportion: more men → less time
- Use: $ M_1 \times D_1 = M_2 \times D_2 $
- $ 36 \times 25 = 15 \times D_2 $
- $ D_2 = \frac{36 \times 25}{15} = \frac{900}{15} = 60 $
✔ Answer: 60 days

#### 5. A workforce of 50 men can finish a piece of work in 5 months. In how many months can 125 men complete the same work?
- Inverse proportion: more men → less time
- $ 50 \times 5 = 125 \times D $
- $ D = \frac{250}{125} = 2 $
✔ Answer: 2 months

#### 6. A workforce of 420 men can finish work in 9 months. How many extra men must be employed to complete it in 7 months?
- Inverse proportion: fewer days → more men needed
- Let new number of men be $ x $
- $ 420 \times 9 = x \times 7 $
- $ x = \frac{3780}{7} = 540 $
- Extra men = $ 540 - 420 = 120 $
✔ Answer: 120 men

#### 7. 1200 men can finish food in 35 days. How many more men should join so that the same stock lasts 25 days?
- Inverse proportion: more men → food lasts fewer days
- Let total men required = $ x $
- $ 1200 \times 35 = x \times 25 $
- $ x = \frac{42000}{25} = 1680 $
- Additional men = $ 1680 - 1200 = 480 $
✔ Answer: 480 men

#### 8. In a hostel of 50 girls, food lasts for 40 days. If 30 more girls join, how long will provisions last?
- Total girls now = $ 50 + 30 = 80 $
- Inverse proportion: more people → fewer days
- $ 50 \times 40 = 80 \times D $
- $ D = \frac{2000}{80} = 25 $
✔ Answer: 25 days

#### 9. 55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?
- More cows → less time (inverse)
- $ 55 \times 16 = x \times 10 $
- $ x = \frac{880}{10} = 88 $
✔ Answer: 88 cows

#### 10. 18 men can reap a field in 35 days. How many men are required to reap the same field in 15 days?
- Inverse proportion
- $ 18 \times 35 = x \times 15 $
- $ x = \frac{630}{15} = 42 $
✔ Answer: 42 men

---

✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | Inversely |
| 2 | Directly |
| 3 | Directly |
| 4 | 60 days |
| 5 | 2 months |
| 6 | 120 men |
| 7 | 480 men |
| 8 | 25 days |
| 9 | 88 cows |
| 10 | 42 men |

---

Let me know if you'd like these explained step-by-step or formatted as a printable answer sheet!