# How to find the missing number of a percentage

PercentageMath-home Previous Next Find the missing number in a percent expressionExample (1) 20% of ? = 25Solution:Shortcut method to find the mission number in the given expressio

## Percentage

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## Find the missing number in a percent expression

Example (1) 20% of ? = 25

**Solution**:

### Shortcut method to find the mission number in the given expression for percent

### Alternate method: Unitary method to find the missing number in a expression for percentage

This is called unitary method. In this method, first of value for 1(one) is calculated. Then value is multiplied by required number to get answer. Unitary method is one of the most used methods.

Example (2) 30% of ? = 600

**Solution**:

### Shortcut method to find the mission number in the given expression for percent

### Alternate method: Unitary method to find the missing number in a expression for percentage

### Questions based on finding the missing number in a expression for percentage

Question: (1) 20% of ? = 100

Or, 20% of what number is equal to 100?

**Solution:**

We have to find 20% of ? = 100

### Shortcut method:

We have to find 20% of ? = 100

### Alternate Method: Unitary Method

We have to find 20% of ? = 100

Let, ? = 100

20% of 100 = 20

Now,

20 is the 20% of 100

1 will be the 20% of `100/20=5`

20 will be 20% of 5 × 20 = 100

Thus, required number = 100 **Answer**

Question: (2) 2% of ? = 45

**Solution:**

We have to find 2% of ? = 45

### Shortcut Method

We have to find 2% of ? = 45

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=2, and m = 45 thus y=?

Therefore, `y=(45xx100)/2`

y = 45 × 50

Therefore, y = 2250 **Answer**

### Alternate Method: Unitary Method

We have to find 2% of ? = 45

Let, ? = 100

2% of 100 = 2

Now,

2 is the 2% of 100

1 will be the 2% of `100/2=50`

45 will be 2% of 50 × 45 = 2250

Thus, required number = 2250 **Answer**

Question: (3) 5% of ? = 200

Or, 5% of what is equal to 200?

**Solution:**

We have to find 5% of ? = 200

### Shortcut Method to find the missing number in given expression of percent

We have to find 5% of ? = 200

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=5, and m = 200 thus y=?

Therefore, `y=(200xx100)/5`

y = 200 × 20

Therefore, y = 4000 **Answer**

### Alternate Method: Unitary Method

We have to find 5% of ? = 200

Let, ? = 100

5% of 100 = 5

Now,

5 is the 5% of 100

1 will be the 5% of `100/5=20`

200 will be 5% of 20 × 200 = 4000

Thus, required number = 4000 **Answer**

Question: (4) 13% of ? = 39

Or, 13% of what number is equal to 39 ?

**Solution:**

We have to find 13% of ? = 39

### Shortcut Method to find the missing number in given expression of percent

We have to find 13% of ? = 39

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=13, and m = 39 thus y=?

Therefore, `y=(39xx100)/13`

y = 3 × 100

Therefore, y = 300 **Answer**

### Alternate Method: Unitary Method

We have to find 13% of ? = 39

Let, ? = 100

13% of 100 = 13

Now,

13 is the 13% of 100

1 will be the 13% of `100/13`

39 will be 13% of `100/13xx39`

= 100 × 3 = 300

Thus, required number = 300 **Answer**

Question: (5) 22% of ? = 110

Or, 22% of what number is equal to 110 ?

**Solution:**

We have to find 22% of ? = 110

Let 22% of `y` = 110

`=>22/100xx\y=110`

After cross multiplication

22`y` = 110 × 100

`=> y = (110xx100)/22`

= 5 × 100 = 500

Thus, required number = 500 **Answer**

### Shortcut Method to find the missing number in given expression of percent

We have to find 22% of ? = 110

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=22, and m = 110 thus y=?

Therefore, `y=(110xx100)/22`

y = 5 × 100 = 500

Therefore, y = 500 **Answer**

### Alternate Method: Unitary Method

We have to find 22% of ? = 110

Let, ? = 100

22% of 100 = 22

Now,

22 is the 22% of 100

1 will be the 22% of `100/22`

110 will be 22% of `100/22xx110`

= 100 × 5 = 500

Thus, required number = 500 **Answer**

Question: (6) 13% of ? = 65

Or, 13% of which number will be equal to 65 ?

**Solution:**

### Shortcut Method to find the missing number in given expression of percent

We have to find 13% of ? = 65

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=13, and m = 65 thus y=?

Therefore, `y=(65xx100)/13`

`y` = 5 × 100 = 500

Therefore, required number = 500 **Answer**

### Alternate Method: Unitary Method

We have to find 13% of ? = 65

Let, ? = 100

13% of 100 = 13

Now,

13 is the 13% of 100

1 will be the 13% of `100/13`

65 will be 13% of `100/13xx65`

= 100 × 5 = 500

Thus, required number = 500 **Answer**

Question: (7) 22% of ? = 88

Or, 22% of what number is equal to 88?

**Solution:**

We have to find 22% of ? = 88

### Shortcut Method to find the missing number in given expression of percent

We have to find 22% of ? = 88

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=22, and m = 88 thus y=?

Therefore, `y=(88xx100)/22`

`y` = 4 × 100 = 400

Therefore, required number = 400 **Answer**

### Alternate Method: Unitary Method

We have to find 22% of ? = 88

Let, ? = 100

22% of 100 = 22

Now,

22 is the 22% of 100

1 will be the 22% of `100/22`

88 will be 22% of `100/22xx88`

= 100 × 4 = 400

Thus, required number = 400 **Answer**

Question: (8) 12% of what number is equal to 60?

**Solution:**

We have to find 12% of ? = 60

### Shortcut Method to find the missing number in given expression of percent

We have to find 12% of ? = 60

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=12, and m = 60 thus y=?

Therefore, `y=(60xx100)/12`

`y` = 5 × 100 = 500

Therefore, required number = 500 **Answer**

### Alternate Method: Unitary Method

We have to find 12% of ? = 60

Let, ? = 100

12% of 100 = 12

Now,

12 is the 12% of 100

1 will be the 12% of `100/12`

60 will be 22% of `100/12xx60`

= 100 × 5 = 500

Thus, required number = 500 **Answer**

Question: (9) 30% of which number is equal to 25?

**Solution:**

We have to find 30% of ? = 25

### Shortcut Method to find the missing number in given expression of percent

We have to find 30% of ? = 25

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=30, and m = 25 thus y=?

Therefore, `y=(25xx100)/30`

`y=(25xx10)/3=250/3`

`y = 83\1/3`

Therefore, required number `= 83\1/3` or 83.333 **Answer**

### Alternate Method: Unitary Method

We have to find 30% of ? = 25

Let, ? = 100

30% of 100 = 30

Now,

30 is the 30% of 100

1 will be the 30% of `100/30`

25 will be 30% of `100/30xx25`

`=(10xx25)3=83\1/3`

Thus, required number `= 83\1/3` or 83.333 **Answer**

Question: (10) 22% of which number is equal to 440?

**Solution:**

We have to find 22% of ? = 440

### Shortcut Method to find the missing number in given expression of percent

We have to find 22% of ? = 440

We know that, if x% of y = m

Therefore, `y=(mxx100)/x`

Here in the given question, x=22, and m = 440 thus y=?

Therefore, `y=(440xx100)/22`

= 20 × 100 = 2000

Therefore, required number = 2000 **Answer**

### Alternate Method: Unitary Method

We have to find 22% of ? = 440

Let, ? = 100

22% of 100 = 22

Now,

22 is the 22% of 100

1 will be the 22% of `100/22`

440 will be 22% of `100/22xx440`

= 100 × 20 = 2000

Thus, required number = 2000 **Answer**

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