mcqs Math Percentage 105 is what percent of 190? Or, What percent of 190 is equal to 105? 1196

Question: 105 is what percent of 190? Or, What percent of 190 is equal to 105?

(A)  69.08%
(B)  41.45%
(C)  55.26%
(D)  82.89%

Correct Answer 55.26%

Solution And Explanation

Solution

Given number = 190

To find, 105 is what percent of 190?

This question can be written as also

What percent of 190 is equal to 105?

⇒ ?% of 190 = 105

Let ? = m

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

∴ m% of 190 = 105

⇒ m% × 190 = 105

⇒ ^m/₁₀₀ × 190 = 105

⇒ ^{190 m}/₁₀₀ = 105

After cross multiplication, we get

190 m = 105 × 100

After transposing 190 to RHS, we get

m = ^{105 × 100}/₁₉₀

⇒ m = ¹⁰⁵⁰⁰/₁₉₀

⇒ m = 55.26%

Thus, 55.26% of 190 = 105

Thus, Answer = 55.26%

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 190 = 105

Here, we have ? = m

a = 190

And, b = 105

Thus, using formula

⇒ m = ^{105 × 100}/₁₉₀

= ^{105 × 100}/₁₉₀

= ¹⁰⁵⁰⁰/₁₉₀ = 55.26%

Thus, 55.26% of 190 = 105

Thus, 55.26% Answer