Question

In their respective exams, Jonah scored 36 out of 40 and Marcus scored 42 out of 70. Who earned the higher score and what was their score in percentage?

• A. Marcus, $90\%$
• B. Marcus, $60\%$
• C. Jonah, $60\%$
• D. Jonah, $90\%$

Answer 1

The correct option is D Jonah, $90\%$

Jonah scored 36 marks out of a total of 40 marks.

Percentage of marks scored by Jonah $=\frac{\text{Marks scored by Jonah}}{\text{Total marks of Jonah's exam}}\times 100=\frac{36}{40}\times 100=90\%$

Marcus scored 42 marks out of a total of 70 marks.

Percentage of marks scored by Marcus $=\frac{\text{Marks scored by Marcus}}{\text{Total marks of Marcus's exam}}\times 100=\frac{42}{70}\times 100=60\%$

So, Jonah's score is higher than Marcus' score.

$Alternativesolution:$
$Step1:$ Convert their scores into fractions.
Jonah $=\frac{36}{40}$
Marcus $=\frac{42}{70}$

$Step2:$
Let Jonah's grade be $p\%.$
Convert the fractions into percentages.
$\frac{36}{40}=\frac{p}{100}$
Cross multiply the two fractions.
$p\times 40=100\times 36$
$p=\frac{100\times 36}{40}$
$p=\frac{10\times 10\times 9\times 4}{4\times 10}$
$p=90$
$\Rightarrow \frac{36}{40}=\frac{90}{100}=90\%$
Jonah's grade $=90\%$
Let Marcus' grade be $q\%.$
Now, repeat the above process to find the value of $q$ in the equation $\frac{42}{70}=\frac{q}{100}$
$q=\frac{100\times 42}{70}$
$q=60$
$\Rightarrow \frac{42}{70}=\frac{60}{100}=60\%$
Marcus's grade $60\%$

$Step3:$ Compare their percentage scores to see who got more.

Jonah's grade $=90\%$
Marcus' grade $=60\%$
So, Jonah's score is higher than Marcus' score. Marcus got $60\%$ and Jonah got $90\%.$