# Ratios and Percentages

Comparing quantities is easy, each of the quantities is defined to a specific standard and then the comparison between them takes place after that. Comparing quantities can be effectively done by bringing them to a certain standard and then comparing them related to that specified standard. For instance, if we quantify a particular thing with respect to 100 portions of the same thing, this is referred to as percentage comparison. Or else if we compare the two things with respect to each other, then we calculate the ratios of these two quantities.

**Ratio**

In simple terms, comparing Quantity1 with Quantity2 is Ratio. The first quantity(say p) is mentioned in the numerator and the second quantity(say q) is mentioned in the denominator. The way to depict the ratio is **p/q**.

Ratio Formula: Quantity 1/Quantity 2

**Example:**

Quantity1 has 5 portions and Quantity2 has 8 portions. The ratio of both the quantities will be 5:8.

**Percentage**

Comparing Quantity with 100 portions of the same quantity in the denominator is Percentage. The first quantity(say p) is mentioned in the numerator and the second quantity(say q) is mentioned in the denominator. This quantity when multiplied by 100. The way to depict the ratio is **(p/q)*100**.

Percentage Formula: (Quantity/Total Quantity) * 100

**Example: **

Quantity1 has 5 portions and Quantity2 has 8 portions.

Percentage of Quantity1: (5/13)*100

Percentage of Quantity2: (8/13)*100

Both are comparing techniques, and are used accordingly in different situations depending on the need.

**Percentage as Fraction:**

80% expressed as fraction will be 80/100

30% expressed as fraction will be 30/100

**Percentage as Ratio:**

80% expressed as ratio will be 80/100 = 4 : 5

30% expressed as ratio will be 30/100 = 3 : 10

**Percentage as Decimal:**

80% expressed as decimal will be 80/100 = 0.8

30% expressed as decimal will be 30/100 = 0.3

**Calculating Percentage of a Number:**

To calculate the percentage, simply multiply the number by the percent.

**Example: **

90% of 10 can be calculated as follows:

(90/100)*10 = 9

So, 90% of 10 is 9.

**Some Quick Formulae**

- If a/b = c/d, then ad = bc
- If a/b = c/d, then b/a = d/c
- If a/b = c/d, then a/c = b/d
- If a/b = c/d, then (a – b)/b = (c – d)/d
- If a/b = c/d, then (a + b)/b = (c + d)/d
- If a/b = c/d, then (a + b)/(a – b) = (c + d)/(c – d), Componendo- Dividendo Rule
- If (a/b)*100 then it’s a/b %

### Practice Problems

**Question 1: A quantity is 25% of 200. Find the quantity?**

**Solution:**

Quantity = (25/100) * 200 = 50

**Question 2: If 60% of a quantity(x) is 300, then find the quantity x?**

**Solution:**

60x/100 = 300

=> x = 30000/60 = 500

The quantity x is 500.

**Question 3: A cricket team won 3 matches out of a total of 5 matches in a series. Depict the winning ratio and percentage?**

**Solution**:

Winning Ratio: 3/5

Winning Percentage: (3/5) * 100 = 60%

**Question 4: Winning percentage of a cricket match series is 60%. Find the total matches won out of 5 in the cricket series?**

**Solution:**

Matches Won = (60/100) * 5 = 3

**Question 5: A nursery has 10000 plants. 10% of the plants are oranges and 3% are mangos plants. What is the total number of other plants?**

**Solution: **

Total Plants = 10000

Orange plants = 10% of total

Mango Plants = 3% of total

Other plants = 100% – (10% + 3%) = 87% of total

= (87/100) * 10000

= 8700

The total number of other plants are 8700.

**Question 6: GeeksforGeeks has 90 engineer employees. In this company, engineers constitute 50% of its workforce. How many people are employed in the company?**

**Solution:**

50% of total workforce = 90 engineers

Let total workforce be x

Then, (50/100) * x = 90

x = (90 * 100) / 50

x = 180

So, the total workforce of GeeksforGeeks is 180 employees.

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