Percentage
MCQs Math

Question:   ( 1 of 10 )  65 is what percent of 110? Or, What percent of 110 is equal to 65?

You selected   88.64%

Correct Answer  59.09%

Solution And Explanation

Solution

Given number = 110

To find, 65 is what percent of 110?

This question can be written as also

What percent of 110 is equal to 65?

⇒ ?% of 110 = 65

Let ? = m

And the meaning of "of" in mathematics is "Multiplication".

∴ m% of 110 = 65

⇒ m% × 110 = 65

⇒ ^m/₁₀₀ × 110 = 65

⇒ ^{110 m}/₁₀₀ = 65

After cross multiplication, we get

110 m = 65 × 100

After transposing 110 to RHS, we get

m = ^{65 × 100}/₁₁₀

⇒ m = ⁶⁵⁰⁰/₁₁₀

⇒ m = 59.09%

Thus, 59.09% of 110 = 65

Thus, Answer = 59.09%

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 110 = 65

Here, we have ? = m

a = 110

And, b = 65

Thus, using formula

⇒ m = ^{65 × 100}/₁₁₀

= ^{65 × 100}/₁₁₀

= ⁶⁵⁰⁰/₁₁₀ = 59.09%

Thus, 59.09% of 110 = 65

Thus, 59.09% Answer