Question : 90 is what percent of 160? Or, What percent of 160 is equal to 90?
Correct Answer 56.25%
Solution & Explanation
Solution
Given number = 160
To find, 90 is what percent of 160?
This question can be written as also
What percent of 160 is equal to 90?
⇒ ?% of 160 = 90
Let ? = m
And the meaning of "of" in mathematics is "Multiplication".
∴ m% of 160 = 90
⇒ m% × 160 = 90
⇒ m/100 × 160 = 90
⇒ 160 m/100 = 90
After cross multiplication, we get
160 m = 90 × 100
After transposing 160 to RHS, we get
m = 90 × 100/160
⇒ m = 9000/160
⇒ m = 56.25%
Thus, 56.25% of 160 = 90
Thus, Answer = 56.25%
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 160 = 90
Here, we have ? = m
a = 160
And, b = 90
Thus, using formula
⇒ m = 90 × 100/160
= 90 × 100/160
= 9000/160 = 56.25%
Thus, 56.25% of 160 = 90
Thus, 56.25% Answer
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