Question

A man got 392 marks out of 460 marks.Find percentage marks obtained by him.\[\]

Answer 1

Hint:We know that If we have $a$ number of elements and there are total $b$ number of elements then we can express $a$as a percentage $p$ of $b$ using the working rule $p=\dfrac{a}{b}\times 100$. We assume marks scored as $a$ and maximum marks as $b$ and then the required percentage using the working rule.\[\]

Complete step by step answer:
We know that percentage is derived from the word per centum in Latin which means per hindered. The percentage in mathematics is a number or ratio expressed as a fraction of 100. If we have $a$ number of elements and there are total $b$ number of elements then we can express $a$ as a percentage $p$ of $b$ using the working rule,
\[p=\dfrac{a}{b}\times 100\]
We denote the percentage of $p$ as $p \%$ where ‘%’ is a symbol of percentage. If we say $p \% $ of $x$ that means if we divide $x$ into hundreds we can allocate $p$ in each of the hundred, for example, 45% of 200 means we can allocate 45 for each hundred in 200. We can calculate the allocation $y$using the rule,
\[y=\dfrac{p}{100}\times x\]
A percentage is primarily used for comparison with different denominators infractions, for example, if we say two students from different schools mays have different maximum marks. If student A has scored 533 marks out of 600 and student B has scored 407 marks out of 500 then we can only compare their score using percentages.
We are given in the question that the man has scored 392 marks. Let us denote the marks scored as $a$, so $a=392$. The maximum marks are 460. Let us denote the maximum marks as $b$, so $a=460$. So the marks scored as percentage $p$ of the maximum marks is ,
\[p=\dfrac{a}{b}\times 100=\dfrac{392}{460}\times 100=\dfrac{3920}{46}=85.217\]
We round off and find the required percentage as $85.22 \%.$\[\]

Note:
 Percentages are used in financial sector , for example interest rate on loans or deposit banks, tax rate, discounts in shops, rates of inflation etcetera. If we divide a total $x$ into parts $a,b$ then we can express each part as percentage as $ \% a=\dfrac{a}{x}\times 100,\% b=\dfrac{b}{x}\times 100.$