Questions & Answers

Question

Answers

(a). 10

(b). 2

(c). 5

(d). None of these

Answer
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.

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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