mcqs Math Percentage 110 is what percent of 200? Or, What percent of 200 is equal to 110? 1197

Question: 110 is what percent of 200? Or, What percent of 200 is equal to 110?

(A)  68.75%
(B)  41.25%
(C)  55%
(D)  82.5%

Correct Answer 55%

Solution And Explanation

Solution

Given number = 200

To find, 110 is what percent of 200?

This question can be written as also

What percent of 200 is equal to 110?

⇒ ?% of 200 = 110

Let ? = m

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

∴ m% of 200 = 110

⇒ m% × 200 = 110

⇒ ^m/₁₀₀ × 200 = 110

⇒ ^{200 m}/₁₀₀ = 110

After cross multiplication, we get

200 m = 110 × 100

After transposing 200 to RHS, we get

m = ^{110 × 100}/₂₀₀

⇒ m = ¹¹⁰⁰⁰/₂₀₀

⇒ m = 55%

Thus, 55% of 200 = 110

Thus, Answer = 55%

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 200 = 110

Here, we have ? = m

a = 200

And, b = 110

Thus, using formula

⇒ m = ^{110 × 100}/₂₀₀

= ^{110 × 100}/₂₀₀

= ¹¹⁰⁰⁰/₂₀₀ = 55%

Thus, 55% of 200 = 110

Thus, 55% Answer