Question

On the day of the result, Ted got his report card. His sister, who studied in another school, also got her report card surprisingly. And she was jumping around saying she has scored a better total than Ted.

Which parameter would be easier to decide about who has done better?

• A. Fraction of marks obtained out of total marks
• B. Total marks obtained
• C. Percentage of marks obtained
• D. Any parameter is fine

Answer 1

Answer: (C)

Percentage of marks obtained

Since Ted and his sister studied in different schools, there is a possibility that they had a different sum total of the maximum marks.

In other words, Ted could have had $9$ papers for $100$ marks each, which means that the total score would be out of $900$.

His sister could have $6$ papers for $100$ marks each. In this case, the sum total will be $600$ marks.

Ted has a possibility of scoring a total of $630$ marks, whereas his sister cannot score $630$ marks.

Thus, to compare their performances, we need a common parameter.

That is why we convert their scores to percentages. So, if Ted scores $630$ out of $900$ (in all papers put together), the score would be $\frac{630}{900}$. To convert that into percentage, the denominator has to be $100$. Thus, $\frac{630}{900}=\frac{70}{100}=70$.

Now, if Ted's sister scores are better than Ted, then her score must be greater than $70\%$.

Which means if her score is $x$ out of $600$, then $\frac{x}{600}>\frac{70}{100}$

$\Rightarrow x>\frac{600\times 70}{100}$

$\Rightarrow x>420$

Thus, his sister has a score above $420$ out of $600$.

Though the total of Ted's sister is below Ted's total marks, her performance is better than Ted's, since we compare their percentages.