In an engineering college, there are four branches namely Computer Science (CS), Electronics (EC), Civil (CE), and Mechanical (ME). The respective ratio of the number of students in these branches is 11 : 5 : 6 : 7. What is the percentage of students belonging to CS and ME branches in the college (correct up to two decimal places)?

Correct Answer: Option 4 (62.07%)

Step-by-Step Explanation:

Step 1: Understand the given ratio of students
The ratio of the number of students in the four branches—Computer Science (CS), Electronics (EC), Civil (CE), and Mechanical (ME)—is given as:
CS : EC : CE : ME = 11 : 5 : 6 : 7

Let the common ratio multiplier be $x$. Therefore, the number of students in each branch is:
$CS=11x$
$EC=5x$
$CE=6x$
$ME=7x$

Step 2: Calculate the total number of students in the college
The total number of students across all four branches is:
$\text{Total students}=11x+5x+6x+7x=29x$

Step 3: Calculate the combined number of students in CS and ME branches
The number of students in CS and ME branches together is:

Step 4: Calculate the required percentage
The percentage of students belonging to CS and ME branches is:
$\text{Percentage}=\left(\frac{18x}{29x}\right)\times 100$
$\text{Percentage}=\frac{1800}{29}\%$

Performing the division:
$1800÷29\approx 62.0689\%$

Rounding off to two decimal places, we get 62.07%.