Class 7 Percentage worksheet with math problems and multiple-choice options for practice.

Let's solve the problems step by step.

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Problem (1):

Calculate: \( (7\% \text{ of } 90) - (90\% \text{ of } 7) \)

#### Solution:
1. Calculate \( 7\% \text{ of } 90 \):
\[
7\% \text{ of } 90 = \frac{7}{100} \times 90 = 0.07 \times 90 = 6.3
\]

2. Calculate \( 90\% \text{ of } 7 \):
\[
90\% \text{ of } 7 = \frac{90}{100} \times 7 = 0.9 \times 7 = 6.3
\]

3. Subtract the two results:
\[
(7\% \text{ of } 90) - (90\% \text{ of } 7) = 6.3 - 6.3 = 0
\]

#### Final Answer:
\[
\boxed{0}
\]

---

Problem (2):

Raj obtained a score of 51% in an exam with a total of 459 marks. If Ria gets 702 marks in the same exam, find the percentage obtained by Ria.

#### Solution:
1. First, calculate the total marks Raj scored:
\[
\text{Raj's score} = 51\% \text{ of } 459 = \frac{51}{100} \times 459 = 0.51 \times 459 = 233.09
\]

2. Now, calculate the percentage obtained by Ria:
\[
\text{Percentage obtained by Ria} = \left( \frac{\text{Ria's score}}{\text{Total marks}} \right) \times 100 = \left( \frac{702}{459} \right) \times 100
\]

3. Simplify the fraction:
\[
\frac{702}{459} = \frac{702 \div 9}{459 \div 9} = \frac{78}{51} = \frac{78 \div 3}{51 \div 3} = \frac{26}{17}
\]

4. Convert to a percentage:
\[
\left( \frac{26}{17} \right) \times 100 \approx 152.94\%
\]

#### Final Answer:
\[
\boxed{152.94\%}
\]

---

Problem (3):

Calculate: \( 200\% \text{ of } \left( \frac{1}{2} \right)^3 \)

#### Solution:
1. Calculate \( \left( \frac{1}{2} \right)^3 \):
\[
\left( \frac{1}{2} \right)^3 = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}
\]

2. Calculate \( 200\% \text{ of } \frac{1}{8} \):
\[
200\% \text{ of } \frac{1}{8} = \frac{200}{100} \times \frac{1}{8} = 2 \times \frac{1}{8} = \frac{2}{8} = \frac{1}{4}
\]

#### Final Answer:
\[
\boxed{\frac{1}{4}}
\]

---

Problem (4):

Convert the following percentages into decimals:
A) \( 0.08\% \)
B) \( 13.4\% \)
C) \( 294\% \)
D) \( 0.3\% \)
E) \( 0.178\% \)
F) \( 3.8\% \)

#### Solution:
To convert a percentage to a decimal, divide by 100.

1. \( 0.08\% = \frac{0.08}{100} = 0.0008 \)
2. \( 13.4\% = \frac{13.4}{100} = 0.134 \)
3. \( 294\% = \frac{294}{100} = 2.94 \)
4. \( 0.3\% = \frac{0.3}{100} = 0.003 \)
5. \( 0.178\% = \frac{0.178}{100} = 0.00178 \)
6. \( 3.8\% = \frac{3.8}{100} = 0.038 \)

#### Final Answers:
\[
\boxed{0.0008, 0.134, 2.94, 0.003, 0.00178, 0.038}
\]

---

Problem (5):

If water expands by 6% of its volume as it freezes, how much ice can be obtained from \( 160 \, \text{m}^3 \) of water?

#### Solution:
1. Let the volume of water be \( V_w = 160 \, \text{m}^3 \).
2. When water freezes, it expands by 6%. The volume of ice \( V_i \) is:
\[
V_i = V_w + 0.06 \times V_w = V_w \times (1 + 0.06) = 160 \times 1.06 = 169.6 \, \text{m}^3
\]

#### Final Answer:
\[
\boxed{169.6 \, \text{m}^3}
\]

---

Problem (6):

If water expands by 2% of its volume as it freezes, how much water is required to obtain \( 81.6 \, \text{m}^3 \) of ice?

#### Solution:
1. Let the volume of water be \( V_w \).
2. When water freezes, it expands by 2%. The volume of ice \( V_i \) is:
\[
V_i = V_w + 0.02 \times V_w = V_w \times (1 + 0.02) = V_w \times 1.02
\]
3. Given \( V_i = 81.6 \, \text{m}^3 \), solve for \( V_w \):
\[
V_w \times 1.02 = 81.6 \implies V_w = \frac{81.6}{1.02} = 80 \, \text{m}^3
\]

#### Final Answer:
\[
\boxed{80 \, \text{m}^3}
\]

---

Problem (7):

If \( 60\% \) of \( a \) is \( 4.2 \), then what is the value of \( a \)?

#### Solution:
1. Given:
\[
60\% \text{ of } a = 4.2 \implies \frac{60}{100} \times a = 4.2 \implies 0.6 \times a = 4.2
\]
2. Solve for \( a \):
\[
a = \frac{4.2}{0.6} = 7
\]

#### Final Answer:
\[
\boxed{7}
\]

---

Problem (8):

What percent of:
A) \( 48 \, \text{hours} \) is \( 2678.4 \, \text{minutes} \)
B) \( 51 \, \text{days} \) is \( 1126.08 \, \text{hours} \)
C) \( 63 \, \text{days} \) is \( 120.96 \, \text{hours} \)
D) \( 65 \, \text{Kg} \) is \( 5050 \, \text{grams} \)
E) \( 88 \, \text{hours} \) is \( 1108.8 \, \text{minutes} \)
F) \( 89 \, \text{hours} \) is \( 3204 \, \text{minutes} \)

#### Solution:
For each part, calculate the percentage using the formula:
\[
\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100
\]

1. A) \( 48 \, \text{hours} \) is \( 2678.4 \, \text{minutes} \):
- Convert \( 48 \, \text{hours} \) to minutes:
\[
48 \, \text{hours} = 48 \times 60 = 2880 \, \text{minutes}
\]
- Calculate the percentage:
\[
\text{Percentage} = \left( \frac{2678.4}{2880} \right) \times 100 \approx 93\%
\]

2. B) \( 51 \, \text{days} \) is \( 1126.08 \, \text{hours} \):
- Convert \( 51 \, \text{days} \) to hours:
\[
51 \, \text{days} = 51 \times 24 = 1224 \, \text{hours}
\]
- Calculate the percentage:
\[
\text{Percentage} = \left( \frac{1126.08}{1224} \right) \times 100 \approx 92\%
\]

3. C) \( 63 \, \text{days} \) is \( 120.96 \, \text{hours} \):
- Convert \( 63 \, \text{days} \) to hours:
\[
63 \, \text{days} = 63 \times 24 = 1512 \, \text{hours}
\]
- Calculate the percentage:
\[
\text{Percentage} = \left( \frac{120.96}{1512} \right) \times 100 \approx 8\%
\]

4. D) \( 65 \, \text{Kg} \) is \( 5050 \, \text{grams} \):
- Convert \( 65 \, \text{Kg} \) to grams:
\[
65 \, \text{Kg} = 65 \times 1000 = 65000 \, \text{grams}
\]
- Calculate the percentage:
\[
\text{Percentage} = \left( \frac{5050}{65000} \right) \times 100 \approx 7.77\%
\]

5. E) \( 88 \, \text{hours} \) is \( 1108.8 \, \text{minutes} \):
- Convert \( 88 \, \text{hours} \) to minutes:
\[
88 \, \text{hours} = 88 \times 60 = 5280 \, \text{minutes}
\]
- Calculate the percentage:
\[
\text{Percentage} = \left( \frac{1108.8}{5280} \right) \times 100 \approx 21\%
\]

6. F) \( 89 \, \text{hours} \) is \( 3204 \, \text{minutes} \):
- Convert \( 89 \, \text{hours} \) to minutes:
\[
89 \, \text{hours} = 89 \times 60 = 5340 \, \text{minutes}
\]
- Calculate the percentage:
\[
\text{Percentage} = \left( \frac{3204}{5340} \right) \times 100 \approx 60\%
\]

#### Final Answers:
\[
\boxed{93\%, 92\%, 8\%, 7.77\%, 21\%, 60\%}
\]

---

Problem (9):

What percentage of the following letters can not be drawn using straight lines?
H I M X D G P

#### Solution:
1. Identify which letters can be drawn using only straight lines:
- H: Can be drawn using straight lines.
- I: Can be drawn using straight lines.
- M: Can be drawn using straight lines.
- X: Can be drawn using straight lines.
- D: Cannot be drawn using only straight lines (curved part).
- G: Cannot be drawn using only straight lines (curved part).
- P: Cannot be drawn using only straight lines (curved part).

2. Total letters: 7
3. Letters that cannot be drawn using straight lines: 3 (D, G, P)
4. Percentage of letters that cannot be drawn using straight lines:
\[
\text{Percentage} = \left( \frac{3}{7} \right) \times 100 \approx 42.86\%
\]

#### Final Answer:
\[
\boxed{42.86\%}
\]

---

Problem (10):

Kareem donated 10% of his salary to charity and spent 30% of the remaining amount. He still has Rs. 7560 left. What was his total salary?

#### Solution:
1. Let Kareem's total salary be \( S \).
2. He donated 10% of his salary to charity:
\[
\text{Remaining salary after donation} = S - 0.1S = 0.9S
\]
3. He spent 30% of the remaining salary:
\[
\text{Amount spent} = 0.3 \times 0.9S = 0.27S
\]
4. The remaining amount after spending is Rs. 7560:
\[
\text{Remaining amount} = 0.9S - 0.27S = 0.63S
\]
5. Set up the equation:
\[
0.63S = 7560
\]
6. Solve for \( S \):
\[
S = \frac{7560}{0.63} = 12000
\]

#### Final Answer:
\[
\boxed{a. Rs.12000}
\]

---

Problem (11):

Alisha has Rs. 4900 with her and spends 36% of it on groceries. How much money is left with her?

#### Solution:
1. Calculate 36% of Rs. 4900:
\[
36\% \text{ of } 4900 = \frac{36}{100} \times 4900 = 0.36 \times 4900 = 1764
\]
2. Subtract the amount spent from the total amount:
\[
\text{Money left} = 4900 - 1764 = 3136
\]

#### Final Answer:
\[
\boxed{a. Rs.3136}
\]

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Final Summary of Answers:

1. \(\boxed{0}\)
2. \(\boxed{152.94\%}\)
3. \(\boxed{\frac{1}{4}}\)
4. \(\boxed{0.0008, 0.134, 2.94, 0.003, 0.00178, 0.038}\)
5. \(\boxed{169.6 \, \text{m}^3}\)
6. \(\boxed{80 \, \text{m}^3}\)
7. \(\boxed{7}\)
8. \(\boxed{93\%, 92\%, 8\%, 7.77\%, 21\%, 60\%}\)
9. \(\boxed{42.86\%}\)
10. \(\boxed{a. Rs.12000}\)
11. \(\boxed{a. Rs.3136}\)