Question

In a test a student got a mark of 49. His report card showed that he had scored 70 percent. What is the maximum mark on the test?
A. 60
B. 70
C. 80
D. None of these

Answer 1

Hint: To solve the question we have the simple idea about percentage. At first we have to consider the total mark of the test to be x. We must convert the given percent into fraction and multiply it by x to get the mark that student scored in terms of x that means if we have say total data of ‘n’ items, and if we take sample of ‘m’ items form total data of ‘n’ items, then sample over total data dives the ratio of amount of sample from total data and when ratio is multiplied by 100, then the expression we get is percentage of sample ‘m’ in total data ‘n’. Finally, we equate the expression obtained to 49 and by solving the equation we can get the value x which is the required answer.

Complete step-by-step answer:
Consider the total mark of the test be x.
We know that a percentage is a number or ratio that represents a fraction of 100. For example 20% represents\[\dfrac{20}{100}\].
Similarly 70% represents\[\dfrac{70}{100}=\dfrac{7}{10}\].
According to the question the report card showed that his score was \[70%\] that means he scored \[70%\]of x. Then his mark is given by\[\dfrac{7}{10}\times x=\dfrac{7x}{10}\].
But given that his mark was 49. Therefore, we get
\[\dfrac{7x}{10}=49\] ……………………………………….. (1)
Now multiplying both the sides of eq. (1) by\[\dfrac{10}{7}\], we will get,
\[\begin{align}
  & \Rightarrow \dfrac{10}{7}\times \dfrac{7x}{10}=\dfrac{10}{7}\times 49 \\
 & \Rightarrow x=70 \\
\end{align}\]
Here we got the total mark of 70.

So, the correct answer is “Option B”.

Note: Percentage has no unit of measurement, but when we calculate percentage always put a sign of % after the final numerical answer. Always remember that we put measure of sample over total data not total data over sample data as this will change the value of ratio, hence percentage will also get changed. Try not to make any calculation mistakes.