Class 6 Percentage worksheet featuring math problems on percentages, conversions, and real-life applications.

Let's solve the problems step by step.

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Problem 1:

When 9 is added to 10% of a number, it gives the number itself. Find the number.

Let the number be \( x \).

According to the problem:
\[ 10\% \text{ of } x + 9 = x \]

This can be written as:
\[ \frac{10}{100}x + 9 = x \]
\[ 0.1x + 9 = x \]

Rearrange the equation to isolate \( x \):
\[ 9 = x - 0.1x \]
\[ 9 = 0.9x \]

Solve for \( x \):
\[ x = \frac{9}{0.9} \]
\[ x = 10 \]

So, the number is:
\[ \boxed{10} \]

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Problem 2:

What percentage of the following letters can be drawn using straight lines?
\[ H, K, X, Z, D, G, Q \]

Letters that can be drawn using straight lines are:
- \( H \)
- \( K \)
- \( X \)
- \( Z \)
- \( D \)

Letters that cannot be drawn using straight lines are:
- \( G \)
- \( Q \)

Total letters = 7
Letters that can be drawn using straight lines = 5

Percentage:
\[ \text{Percentage} = \left( \frac{\text{Number of letters that can be drawn using straight lines}}{\text{Total number of letters}} \right) \times 100 \]
\[ \text{Percentage} = \left( \frac{5}{7} \right) \times 100 \]
\[ \text{Percentage} \approx 71.43\% \]

So, the answer is:
\[ \boxed{71.43\%} \]

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Problem 3:

Find:
A) 8% of 103 meters
B) 0.9% of 60 kg
C) 0.4% of 482 km
D) 10% of 245 litres
E) 7% of 671 litres
F) 50% of 983 seconds

#### A) 8% of 103 meters
\[ 8\% \text{ of } 103 = \frac{8}{100} \times 103 = 0.08 \times 103 = 8.24 \text{ meters} \]

#### B) 0.9% of 60 kg
\[ 0.9\% \text{ of } 60 = \frac{0.9}{100} \times 60 = 0.009 \times 60 = 0.54 \text{ kg} \]

#### C) 0.4% of 482 km
\[ 0.4\% \text{ of } 482 = \frac{0.4}{100} \times 482 = 0.004 \times 482 = 1.928 \text{ km} \]

#### D) 10% of 245 litres
\[ 10\% \text{ of } 245 = \frac{10}{100} \times 245 = 0.1 \times 245 = 24.5 \text{ litres} \]

#### E) 7% of 671 litres
\[ 7\% \text{ of } 671 = \frac{7}{100} \times 671 = 0.07 \times 671 = 46.97 \text{ litres} \]

#### F) 50% of 983 seconds
\[ 50\% \text{ of } 983 = \frac{50}{100} \times 983 = 0.5 \times 983 = 491.5 \text{ seconds} \]

So, the answers are:
\[ \boxed{8.24, 0.54, 1.928, 24.5, 46.97, 491.5} \]

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Problem 4:

Convert the following to decimal:
A) 72%
B) 127%
C) 87.1%
D) 75%
E) 109%
F) 34%

#### A) 72%
\[ 72\% = \frac{72}{100} = 0.72 \]

#### B) 127%
\[ 127\% = \frac{127}{100} = 1.27 \]

#### C) 87.1%
\[ 87.1\% = \frac{87.1}{100} = 0.871 \]

#### D) 75%
\[ 75\% = \frac{75}{100} = 0.75 \]

#### E) 109%
\[ 109\% = \frac{109}{100} = 1.09 \]

#### F) 34%
\[ 34\% = \frac{34}{100} = 0.34 \]

So, the answers are:
\[ \boxed{0.72, 1.27, 0.871, 0.75, 1.09, 0.34} \]

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Problem 5:

Calculate:
\[ (100\% \text{ of } Rs.\,4) + (4\% \text{ of } Rs.\,100) + Rs.\,4 = ? \]

#### Step 1: Calculate 100% of Rs. 4
\[ 100\% \text{ of } Rs.\,4 = \frac{100}{100} \times 4 = 4 \]

#### Step 2: Calculate 4% of Rs. 100
\[ 4\% \text{ of } Rs.\,100 = \frac{4}{100} \times 100 = 4 \]

#### Step 3: Add all the values
\[ 4 + 4 + 4 = 12 \]

So, the answer is:
\[ \boxed{12} \]

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Problem 6:

An article with a price tag of Rs. 200 is sold at a 20% discount. Due to the festival season, the shopkeeper provides an additional discount of 50% on the discounted price. Find the selling price of the article.

#### Step 1: Calculate the price after the first discount (20% off)
\[ \text{Discount} = 20\% \text{ of } 200 = \frac{20}{100} \times 200 = 40 \]
\[ \text{Price after first discount} = 200 - 40 = 160 \]

#### Step 2: Calculate the price after the second discount (50% off)
\[ \text{Discount} = 50\% \text{ of } 160 = \frac{50}{100} \times 160 = 80 \]
\[ \text{Price after second discount} = 160 - 80 = 80 \]

So, the selling price is:
\[ \boxed{80} \]

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Problem 7:

Tina donated 20% of her salary to charity and spent 20% of the remaining amount. She still has Rs. 7040 left. What was her total salary?

Let Tina's total salary be \( x \).

#### Step 1: Calculate the amount donated to charity
\[ \text{Amount donated} = 20\% \text{ of } x = \frac{20}{100}x = 0.2x \]
\[ \text{Remaining amount after donation} = x - 0.2x = 0.8x \]

#### Step 2: Calculate the amount spent from the remaining amount
\[ \text{Amount spent} = 20\% \text{ of } 0.8x = \frac{20}{100} \times 0.8x = 0.2 \times 0.8x = 0.16x \]
\[ \text{Amount left} = 0.8x - 0.16x = 0.64x \]

#### Step 3: Set up the equation
\[ 0.64x = 7040 \]

Solve for \( x \):
\[ x = \frac{7040}{0.64} = 11000 \]

So, Tina's total salary is:
\[ \boxed{11000} \]

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Problem 8:

Convert the following percent into decimal:
A) 0.08%
B) 196%
C) 2.08%
D) 2.66%
E) 0.098%
F) 1.32%

#### A) 0.08%
\[ 0.08\% = \frac{0.08}{100} = 0.0008 \]

#### B) 196%
\[ 196\% = \frac{196}{100} = 1.96 \]

#### C) 2.08%
\[ 2.08\% = \frac{2.08}{100} = 0.0208 \]

#### D) 2.66%
\[ 2.66\% = \frac{2.66}{100} = 0.0266 \]

#### E) 0.098%
\[ 0.098\% = \frac{0.098}{100} = 0.00098 \]

#### F) 1.32%
\[ 1.32\% = \frac{1.32}{100} = 0.0132 \]

So, the answers are:
\[ \boxed{0.0008, 1.96, 0.0208, 0.0266, 0.00098, 0.0132} \]

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Problem 9:

2.4 is what percent of 600?

Let the percentage be \( p \).

\[ 2.4 = \frac{p}{100} \times 600 \]

Solve for \( p \):
\[ p = \frac{2.4 \times 100}{600} = \frac{240}{600} = 0.4 \]

So, the percentage is:
\[ \boxed{0.4\%} \]

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Problem 10:

If \( x \) is 10% less than \( y \), then \( y \) is more than \( x \) by what percentage?

Let \( x = y - 10\% \text{ of } y \).

\[ x = y - \frac{10}{100}y = y - 0.1y = 0.9y \]

Now, find how much more \( y \) is than \( x \):
\[ y - x = y - 0.9y = 0.1y \]

The percentage increase from \( x \) to \( y \) is:
\[ \text{Percentage increase} = \left( \frac{y - x}{x} \right) \times 100 = \left( \frac{0.1y}{0.9y} \right) \times 100 = \frac{0.1}{0.9} \times 100 = \frac{10}{9} \approx 11.11\% \]

So, the answer is:
\[ \boxed{\frac{1}{9}\%} \]

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Problem 11:

_ % of 160 + 45% of 920 = 510. Find the missing number.

Let the missing percentage be \( p \).

\[ \frac{p}{100} \times 160 + \frac{45}{100} \times 920 = 510 \]

Simplify:
\[ \frac{p}{100} \times 160 + 414 = 510 \]
\[ \frac{p}{100} \times 160 = 510 - 414 \]
\[ \frac{p}{100} \times 160 = 96 \]
\[ p \times 160 = 96 \times 100 \]
\[ p = \frac{96 \times 100}{160} = 60 \]

So, the missing percentage is:
\[ \boxed{60} \]

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Final Answers:

1. \( \boxed{10} \)
2. \( \boxed{71.43\%} \)
3. \( \boxed{8.24, 0.54, 1.928, 24.5, 46.97, 491.5} \)
4. \( \boxed{0.72, 1.27, 0.871, 0.75, 1.09, 0.34} \)
5. \( \boxed{12} \)
6. \( \boxed{80} \)
7. \( \boxed{11000} \)
8. \( \boxed{0.0008, 1.96, 0.0208, 0.0266, 0.00098, 0.0132} \)
9. \( \boxed{0.4\%} \)
10. \( \boxed{\frac{1}{9}\%} \)
11. \( \boxed{60} \)