Question : 165 is what percent of 310? Or, What percent of 310 is equal to 165?
Correct Answer 53.23%
Solution & Explanation
Solution
Given number = 310
To find, 165 is what percent of 310?
This question can be written as also
What percent of 310 is equal to 165?
⇒ ?% of 310 = 165
Let ? = m
And the meaning of "of" in mathematics is "Multiplication".
∴ m% of 310 = 165
⇒ m% × 310 = 165
⇒ m/100 × 310 = 165
⇒ 310 m/100 = 165
After cross multiplication, we get
310 m = 165 × 100
After transposing 310 to RHS, we get
m = 165 × 100/310
⇒ m = 16500/310
⇒ m = 53.23%
Thus, 53.23% of 310 = 165
Thus, Answer = 53.23%
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 310 = 165
Here, we have ? = m
a = 310
And, b = 165
Thus, using formula
⇒ m = 165 × 100/310
= 165 × 100/310
= 16500/310 = 53.23%
Thus, 53.23% of 310 = 165
Thus, 53.23% Answer
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