Answer

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**Hint:**We use the concept of percentage to find percentage of Raju. Write marks obtained and total marks in form of fraction and convert the fraction into percentage by multiplying the fraction by 100.

* Percentage is a part of a whole or complete. Percentage is always greater than or equal to 0% and always less than or equal to 100%.

**Complete step-by-step answer:**

We are given total marks as 600

Number of marks obtained by Raju is 540

We know percentage of marks obtained by a student is given by

Number of marks obtained divided by total marks \[ \times 100\]

Substitute the value of marks obtained by Raju in numerator and total marks in denominator.

\[ \Rightarrow \]Percentage of marks obtained by Raju\[ = \left( {\dfrac{{540}}{{600}} \times 100} \right)\% \]

We write denominator in terms of its factors so we can cancel out factors from numerator and denominator.

We can write \[600 = 6 \times 100\]

\[ \Rightarrow \]Percentage of marks obtained by Raju\[ = \left( {\dfrac{{540}}{{6 \times 100}} \times 100} \right)\% \]

Cancel same terms from numerator and denominator

\[ \Rightarrow \]Percentage of marks obtained by Raju\[ = \left( {\dfrac{{540}}{6}} \right)\% \]

Write the numerator in terms of its factor so we can cancel factors that are in denominator and numerator.

We can write \[540 = 6 \times 90\]

Substitute the value of 540 in numerator

\[ \Rightarrow \]Percentage of marks obtained by Raju\[ = \left( {\dfrac{{6 \times 90}}{6}} \right)\% \]

Cancel same factor i.e. 6 from both numerator and denominator.

\[ \Rightarrow \]Percentage of marks obtained by Raju\[ = 90\% \]

**Thus, the percentage of marks scored by Raju is 90%**

**Note:**Students might make the mistake of not converting the fraction into simpler form. Keep in mind always cancel all factors between numerator and denominator, else the percentage will not be within 0 and 100. Also, when converting percentage into fraction, we divide the number given in percentage by 100.

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