**Percentage is a way of expressing a quantity or amount as a fraction of 100. **

**It is represented by the symbol “%”. **

**For example, if you scored 85 out of 100 in a test, your percentage score would be 85%.**

**To express percentages in fractions, simply divide the percentage by 100 and simplify the resulting fraction if possible. **

**For example:**

**25% = 25/100 = 1/4**

**75% = 75/100 = 3/4**

**60% = 60/100 = 3/5**

**10% = 10/100 = 1/10**

**To express percentages in decimals, simply divide the percentage by 100. **

**For example:**

**25% = 25/100 = 0.25**

**75% = 75/100 = 0.75**

**60% = 60/100 = 0.60**

**10% = 10/100 = 0.10**

**Let’s Do Some PracticeÂ **

**1.Express 40% as a fraction and a decimal.**

**Solution:**

**40% = 40/100 = 2/5 = 0.40**

**2.Express 125% as a fraction and a decimal.**

**Solution: **

**125% = 125/100 = 5/4 = 1.25**

**3.Express 3/5 as a percentage and a decimal.**

**Solution: **

**3/5 = 60/100 = 60% = 0.60**

**4.Express 0.75 as a percentage and a fraction.**

**Solution: **

**0.75 = 75/100 = 75% = 3/4**

**5.Express 1/8 as a percentage and a decimal.**

**Solution: **

**1/8 = 12.5% = 0.125**

**6.Express 80% as a fraction and a decimal.**

**Solution: **

**80% = 80/100 = 4/5 = 0.80**

**7.Express 5/6 as a percentage and a decimal.**

**Solution: **

**5/6 = 83.33% = 0.8333**

**8.Express 150% as a fraction and a decimal.**

**Solution: **

**150% = 150/100 = 3/2 = 1.50**

**9.Express 0.125 as a percentage and a fraction.**

**Solution: **

**0.125 = 12.5% = 1/8**

**10.Express 0.4 as a percentage and a fraction.**

**Solution: **

**0.4 = 40% = 2/5**

**11.Express 2.5% as a fraction and a decimal.**

**Solution: **

**2.5% is equivalent to 2.5/100, which can be simplified to 1/40 as a fraction.**

**As a decimal, 2.5% is equal to 0.025.**

**12.Express 60% as a fraction and a decimal.**

**Solution: **

**60% is equivalent to 60/100, which can be simplified to 3/5 as a fraction. **

**As a decimal, 60% is equal to 0.6.**

**Now General Percentage Problems**

**Requested By:**

**Question 1:**

**What percentage is equivalent to 3/4?**

**Solution: **

**We can set up a proportion: x/100 = 3/4, **

**where x is the percentage we’re trying to find. Cross-multiplying, **

**we get 4x = 300, so x = 75%. **

**Therefore, 3/4 is equivalent to 75%.**

**Requested by: AsifÂ **

**Question 2:**

**If 40% of a number is 24, what is the number?**

**Solution: **

**We can set up a proportion: 40/100 = 24/x, **

**where x is the number we’re trying to find. **

**Cross-multiplying, **

**we get 40x = 2400, so x = 60. **

**Therefore, the number is 60.**

**Requested by: Ahmed Ali**

**Question 3:**

**What is 15% of 80?**

**Solution: **

**To find 15% of 80, **

**we can multiply 80 by 0.15.**

**This gives us 12.**

**Requested by: Ahmed Ali**

**Question 4:**

**If a pizza has 12 slices and a person eats 3 slices, what percentage of the pizza did they eat?**

**Solution: **

**To find the percentage, we can divide the number of slices eaten by the total number of slices and then multiply by 100. **

**This gives us (3/12) x 100 = 25%. **

**Therefore, the person ate 25% of the pizza.**

**Requested by: Ali Nawaz**

**Question 5:**

**A recipe calls for 1/2 cup of sugar for every 2 cups of flour. What percentage of the recipe is sugar?**

**Solution: **

**To find the percentage, we can divide the amount of sugar by the total amount of ingredients (sugar + flour) and then multiply by 100. **

**This gives us (1/2) / (1/2 + 2) x 100 = 20%. **

**Therefore, sugar makes up 20% of the recipe.**

Requested by: Ali Nawaz

Requested by: Ali Nawaz

**Question 6:**

**A recipe calls for 3/4 cup of milk for every 1 cup of flour. What percentage of the recipe is milk?**

**Solution: **

**To find the percentage, we can divide the amount of milk by the total amount of ingredients (milk + flour) and then multiply by 100. **

**This gives us (3/4) / (3/4 + 1) x 100 = 42.86% (rounded to two decimal places). **

**Therefore, milk makes up 42.86% of the recipe.**

**Requested by: Ali Nawaz**

**Question 7:**

**A pizza has 8 slices and a person eats 2 slices. What percentage of the pizza did they eat?**

**Solution: **

**To find the percentage, we can divide the number of slices eaten by the total number of slices and then multiply by 100.**

**This gives us (2/8) x 100 = 25%.**

**Therefore, the person ate 25% of the pizza.**

**Requested by: Ali Nawaz**

**Question 8:**

**A recipe calls for 2 cups of flour and 1 cup of sugar. If a baker wants to make a smaller batch using only 1 cup of flour, how much sugar should they use?**

**Answer:**

**(1/2 x 1 = 0.5)**

The baker should use 0.5 cups of sugar

Requested by: Meer Muhammad

The baker should use 0.5 cups of sugar

Requested by: Meer Muhammad

**Question 9:**

**A car rental company charges $50 per day for a rental car, with an additional charge of 10 cents per mile driven. **

**If a customer rents a car for 3 days and drives 150 miles, how much will they be charged?**

**Answer: **

**($50 x 3 + $0.10 x 150 = $65)**

The customer will be charged $65

Requested by: Sarfaraz Ahmed

The customer will be charged $65

Requested by: Sarfaraz Ahmed

**Now to find out **

**New Price/Sale Price**

**Question 1:**

**If a shirt originally costs $40 and is now on sale for 20% off, what is the new price?**

**Solution: **

**The discount is 20% of $40, which is $8.**

**Therefore, the new price is $40 – $8 = $32.**

**Requested by: Asim**

**Question 2:**

**A shirt that was originally priced at $50 is now on sale for 20% off. What is the sale price?**

**Answer: **

**($50 – (20% x $50) = $40).**

**The sale price of the shirt is $40**

Requested by: Asim

Requested by: Asim

**Question 3:**

**A car dealership offers a 5% discount on all new cars. If a car costs $25,000, what is the sale price?**

**Solution: **

**The discount is 5% of $25,000, which is $1,250. **

**So,the sale price is $25,000 – $1,250 = $23,750.**

**Requested by: Aakash Kumar**

**Question 4:**

**A store has a sale where all items are 20% off. If a shirt originally costs $30, what is the sale price?**

**Solution: **

**The discount is 20% of $30, which is $6. **

**Therefore, the sale price is $30 – $6 = $24.**

**Alternative Method**

**A store has a sale where all items are 30% off. If a book originally costs $20, what is the sale price?**

**Answer: The sale price of the book is $14 **

**Requested by: Asad**

**Question 5:**

**A movie theater has a seating capacity of 500 people. If 80% of the seats are filled for a particular movie, how many people are in the audience?**

**Solution: **

**There are 500 x 0.80 = 400 people in the audience.**

**Requested by: Ameer Bux**

**Question 6:**

**If 15% of the people in a city are over the age of 65, and there are 300,000 people living in the city, how many people are over the age of 65?**

**Answer: **

**(15% x 300,000 = 45,000).**

There are 45,000 people over the age of 65

Requested by: Ameer Bux

There are 45,000 people over the age of 65

Requested by: Ameer Bux

**Question 7:**

**A company has 100 employees, 60% of whom are women. How many of the employees are women?**

**Answer: **

**(60% x 100 = 60)**

There are 60 women employees

Requested by: Ameer Bux

There are 60 women employees

Requested by: Ameer Bux

**Question 8:**

**A gym membership costs $60 per month. If a member gets a 10% discount for paying for 6 months in advance, how much will they save?**

**Solution: **

**The discount is 10% of 6 months’ worth of membership fees, which is $60 x 6 x 0.10 = $36. **

**Therefore, the member will save $36.**

**Requested by: Daniyal**

**Question 9:**

**A restaurant’s food cost is 30% of its revenue. If the restaurant’s revenue last month was $50,000, how much did they spend on food cost?**

**Solution: **

**The food cost is 30% of $50,000, which is $15,000. **

**Therefore, the restaurant spent $15,000 on food cost.**

**Requested by: Aamir**

**Question 10:**

**A company has 500 employees, and 60% of them have been with the company for more than 5 years. **

**How many employees have been with the company for more than 5 years?**

**Solution: **

**There are 500 x 0.60 = 300 employees who have been with the company for more than 5 years.**

**Requested by: Muneeb**

**Question 11:**

**If a car depreciates by 15% each year, how much will it be worth after 3 years if its original value was $20,000?**

**Solution:**

**After one year, the car will be worth 85% of its original value, or $17,000. **

**After two years, it will be worth 85% of $17,000, or $14,450. **

**After three years, it will be worth 85% of $14,450, or $12,282.50.**

**Requested by: Aayan**

**Question 12:**

**If a company’s profits increase by 25% from one year to the next, what is the new profit if the original profit was $10,000?**

**Solution: **

**The increase in profits is 25% of $10,000, which is $2,500. **

**Therefore, the new profit is $10,000 + $2,500 = $12,500.**

**Requested by: Muhammad Ali**

**Question 13:**

**If a company’s revenue was $500,000 last year and it increased by 15% this year, what is the new revenue?**

**Solution: **

**The increase in revenue is 15% of $500,000, which is $75,000. **

**Therefore, the new revenue is $500,000 + $75,000 = $575,000.**

**Requested by: Muhammad Ubaid**

**Question 14:**

**If a company’s profit margin is 20%, and its revenue last year was $1,000,000, **

**how much profit did the company make?**

**Solution: **

**The profit is 20% of $1,000,000, which is $200,000. **

**Therefore, the company made $200,000 in profit.**

**Requested by: Aqib**

**Question 15:**

**If a company’s expenses for the year were $1,000,000 and their revenue was $1,200,000, **

**what was their profit margin as a percentage?**

**Answer: (($1,200,000 – $1,000,000) / $1,200,000 x 100 = 20%)**

**The company’s profit margin was 20%**

Requested by: Faizan

Requested by: Faizan

**Question 16:**

**If a recipe calls for 2 cups of sugar for every 3 cups of flour, what is the sugar-to-flour ratio as a percentage?**

**Solution: **

**The sugar-to-flour ratio is 2:3. ****To express this as a percentage, **

**we can add the two numbers in the ratio (2 + 3 = 5) **

**and then divide each number by the sum and multiply by 100. **

**This gives us (2/5) x 100 = 40%.**

**Requested by: Anwar**

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