Question : 5 is what percent of 78? Or, What percent of 78 is equal to 5?
Correct Answer 6.41%
Solution & Explanation
Solution
Method (1)
Given number = 78
To find, 5 is what percent of 78?
This question can be written as also
What percent of 78 is equal to 5?
⇒ ?% of 78 = 5
Let ? = m
And the meaning of "of" in mathematics is "Multiplication".
∴ m% of 78 = 5
⇒ m% × 78 = 5
⇒ m/100 × 78 = 5
⇒ 78 m/100 = 5
After cross multiplication, we get
78 m = 5 × 100
After transposing 78 to RHS, we get
m = 5 × 100/78
⇒ m = 500/78
⇒ m = 6.41%
Thus, 6.41% of 78 = 5
Thus, Answer = 6.41%
Method (2) Shortcut Method
Shortcut Method to find a number is what percent of other
If we have to find
? % of a = b
Here, let ? = m
Thus, above expression can be written as
m% of a = b
⇒ m/100 × a = b
⇒ m × a/100 = b
After cross multiplication, we get
m × a = b × 100
⇒ m = b × 100/a
Thus, using this formula, we can find a number (a) is what (m) percent of b
In the question, we have to find what percent of 78 = 5
Here, we have ? = m
a = 78
And, b = 5
Thus, using formula
⇒ m = 5 × 100/78
= 5 × 100/78
= 500/78 = 6.41%
Thus, 6.41% of 78 = 5
Thus, 6.41% Answer
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