Percentage - Arithmetic
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
∴ 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,
Here in the given question, x=2, and m = 45 thus y=?
Therefore,
⇒ 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
∴ 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,
Here in the given question, x=5, and m = 200 thus y=?
Therefore,
⇒ 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
∴ 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,
Here in the given question, x=13, and m = 39 thus y=?
Therefore,
⇒ 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
∴ 39 will be 13% of
= 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
After cross multiplication
⇒ 22y = 110 × 100
= 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,
Here in the given question, x=22, and m = 110 thus y=?
Therefore,
⇒ 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
∴ 110 will be 22% of
= 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,
Here in the given question, x=13, and m = 65 thus y=?
Therefore,
⇒ 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
∴ 65 will be 13% of
= 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,
Here in the given question, x=22, and m = 88 thus y=?
Therefore,
⇒ 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
∴ 88 will be 22% of
= 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,
Here in the given question, x=12, and m = 60 thus y=?
Therefore,
⇒ 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
∴ 60 will be 22% of
= 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,
Here in the given question, x=30, and m = 25 thus y=?
Therefore,
⇒
Therefore, required number
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
∴ 25 will be 30% of
Thus, required number
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,
Here in the given question, x=22, and m = 440 thus y=?
Therefore,
= 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
∴ 440 will be 22% of
= 100 × 20 = 2000
Thus, required number = 2000 Answer
Reference: