If x % of 200 is 10, then what is the value of x.
(a). 10
(b). 2
(c). 5
(d). None of these

Answer Verified Verified
Hint: Recall the definition of percentage and then find the equation relating x. Solve the equation relating x to find the value of x.

Complete step-by-step answer:

Percentage of a quantity means a fraction of the quantity expressed by taking a hundred as a whole. 100 % means the entire quantity or the whole. The word percent comes from Latin word Per Cent where Centum means hundred.
Percentage is just a convenient way to express a fraction with hundred as a whole.
Percentage is a number expressed as a fraction of 100. It is calculated by multiplying the numeric of the ratio by 100.
To calculate the value of a percentage of some number, we need to multiply that number with the required percentage and divide by 100.
\[{\text{Percentage = }}\dfrac{{{\text{Required value}}}}{{{\text{Total value}}}} \times 100\% \]
Suppose, we have a percentage and want to find the value, we just multiply the percentage with the total quantity and divide by 100.
\[{\text{Required value = }}\dfrac{{{\text{Total value}} \times {\text{Percentage}}}}{{100}}..........(1)\]
Hence, x % of 200 is x multiplied with 200 and divided by 100 and it is given to be 10. Using equation (1), we have as follows:
\[\dfrac{{x \times 200}}{{100}} = 10\]
Solving for x, we get:
\[x \times 2 = 10\]
\[x = \dfrac{{10}}{2}\]
\[x = 5\]
The value of x is 5.
Hence, the correct answer is option (c).

Note: You might choose option (b) as the correct answer if you attempt to solve without using the percentage formula, which is wrong. Remember that percentage is always out of 100.
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