Class 7 Maths Worksheet: Comparing Quantities - Ratio & Proportion

Let's solve each problem step by step:

---

Problem 1: Find the ratio of 2m to 8m.

- The ratio of two quantities is found by dividing one by the other.
- Here, the ratio of \(2 \, \text{m}\) to \(8 \, \text{m}\) is:
\[
\frac{2}{8} = \frac{1}{4}
\]
- Therefore, the ratio is \(1:4\).

Answer: \(1:4\)

---

Problem 2: Find the ratio of 9km to 180m.

- First, convert both quantities to the same unit. Since \(1 \, \text{km} = 1000 \, \text{m}\), we have:
\[
9 \, \text{km} = 9 \times 1000 = 9000 \, \text{m}
\]
- Now, the ratio of \(9000 \, \text{m}\) to \(180 \, \text{m}\) is:
\[
\frac{9000}{180} = \frac{9000 \div 180}{180 \div 180} = \frac{50}{1}
\]
- Therefore, the ratio is \(50:1\).

Answer: \(50:1\)

---

Problem 3: Out of 2:5 and 3:7, which ratio is greater?

- To compare two ratios, we can convert them to decimal form or find a common denominator.
- For \(2:5\):
\[
\frac{2}{5} = 0.4
\]
- For \(3:7\):
\[
\frac{3}{7} \approx 0.4286
\]
- Since \(0.4286 > 0.4\), the ratio \(3:7\) is greater.

Answer: \(3:7\)

---

Problem 4: Out of 6:11 and 9:14, which ratio is greater?

- Again, we can compare these ratios by converting them to decimal form.
- For \(6:11\):
\[
\frac{6}{11} \approx 0.5455
\]
- For \(9:14\):
\[
\frac{9}{14} \approx 0.6429
\]
- Since \(0.6429 > 0.5455\), the ratio \(9:14\) is greater.

Answer: \(9:14\)

---

Problem 5: The length and width of a rectangle are in the ratio 3:5. If its perimeter is 48 cm, find its length.

- Let the length be \(3x\) and the width be \(5x\).
- The perimeter of a rectangle is given by:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
\]
- Substituting the given values:
\[
48 = 2 \times (3x + 5x)
\]
\[
48 = 2 \times 8x
\]
\[
48 = 16x
\]
\[
x = \frac{48}{16} = 3
\]
- The length is \(3x = 3 \times 3 = 9 \, \text{cm}\).

Answer: \(9 \, \text{cm}\)

---

Problem 6: A jet plane requires 600 kg of fuel in 45 minutes. How much fuel would be used for a three-hour flight?

- First, convert three hours to minutes:
\[
3 \, \text{hours} = 3 \times 60 = 180 \, \text{minutes}
\]
- The fuel consumption rate is:
\[
\frac{600 \, \text{kg}}{45 \, \text{minutes}}
\]
- For 180 minutes, the fuel required is:
\[
\text{Fuel} = \left(\frac{600}{45}\right) \times 180 = \frac{600 \times 180}{45} = \frac{108000}{45} = 2400 \, \text{kg}
\]

Answer: \(2400 \, \text{kg}\)

---

Problem 7: The ratio of the number of male and female workers in a factory is 5:3. If there are 150 male workers, determine the number of female workers in the factory.

- Let the number of male workers be \(5x\) and the number of female workers be \(3x\).
- Given that the number of male workers is 150:
\[
5x = 150
\]
\[
x = \frac{150}{5} = 30
\]
- The number of female workers is:
\[
3x = 3 \times 30 = 90
\]

Answer: \(90\)

---

Problem 8: If \((4x + 5):(3x + 11) = 13:17\), find the value of \(x\).

- We are given the proportion:
\[
\frac{4x + 5}{3x + 11} = \frac{13}{17}
\]
- Cross-multiplying gives:
\[
17(4x + 5) = 13(3x + 11)
\]
- Expanding both sides:
\[
68x + 85 = 39x + 143
\]
- Rearranging terms to isolate \(x\):
\[
68x - 39x = 143 - 85
\]
\[
29x = 58
\]
\[
x = \frac{58}{29} = 2
\]

Answer: \(2\)

---

Problem 9: Are 30, 40, 45, 60 in proportion? (Yes/No)

- Four numbers \(a, b, c, d\) are in proportion if:
\[
\frac{a}{b} = \frac{c}{d}
\]
- Here, \(a = 30\), \(b = 40\), \(c = 45\), and \(d = 60\). Check:
\[
\frac{30}{40} = \frac{3}{4} \quad \text{and} \quad \frac{45}{60} = \frac{3}{4}
\]
- Since \(\frac{30}{40} = \frac{45}{60}\), the numbers are in proportion.

Answer: Yes

---

Problem 10: The first three terms of a proportion are 3, 5, and 21 respectively. Find its fourth term.

- In a proportion, if the terms are \(a, b, c, d\), then:
\[
\frac{a}{b} = \frac{c}{d}
\]
- Here, \(a = 3\), \(b = 5\), and \(c = 21\). Let the fourth term be \(d\). Then:
\[
\frac{3}{5} = \frac{21}{d}
\]
- Cross-multiplying gives:
\[
3d = 5 \times 21
\]
\[
3d = 105
\]
\[
d = \frac{105}{3} = 35
\]

Answer: \(35\)

---

Final Answers:

1. \(1:4\)
2. \(50:1\)
3. \(3:7\)
4. \(9:14\)
5. \(9 \, \text{cm}\)
6. \(2400 \, \text{kg}\)
7. \(90\)
8. \(2\)
9. Yes
10. \(35\)

\[
\boxed{1:4, 50:1, 3:7, 9:14, 9, 2400, 90, 2, \text{Yes}, 35}
\]