In a scholarship assessment, Meera scored 60 marks more than Rohan. Meera's score was 70% of their total combined score. Find the marks scored by Rohan and Meera, respectively.

The correct answer is 45 and 105.

Step 1: Understand the given information in terms of percentage
Let the total combined score of Meera and Rohan be 100%.
We are given that Meera's score represents 70% of their total combined score.

Step 2: Calculate Rohan's score percentage
Since the combined score of both students equals 100%, Rohan's share of the total score is:

$\text{Rohan's Percentage}=100\%-70\%=30\%$

Step 3: Determine the percentage difference between their scores
The difference between Meera's score percentage and Rohan's score percentage is:

$\text{Percentage Difference}=70\%-30\%=40\%$

Step 4: Connect the percentage difference to actual marks
We are given that Meera scored 60 marks more than Rohan. Therefore, 40% of the total combined score corresponds to 60 marks.

$40\%\text{of Total Score}=60\text{marks}$

To find how many marks represent 1% of the total score, divide 60 by 40:

$1\%\text{of Total Score}=\frac{60}{40}=1.5\text{marks}$

Step 5: Calculate Rohan's and Meera's individual marks
Now multiply each student's percentage by 1.5 to get their actual marks:

Rohan's score (30% of total score):

$\text{Rohan's Marks}=30\times 1.5=45$

Meera's score (70% of total score):

$\text{Meera's Marks}=70\times 1.5=105$

Alternative Method (Algebraic Approach):
Let Rohan's score be $R$ and Meera's score be $M$.
Given that Meera scored 60 marks more than Rohan:

$M=R+60$

Their total combined score is:

$\text{Total Score}=M+R=(R+60)+R=2R+60$

Since Meera's score is 70% (or 0.70) of the total score:

$R+60=0.70\times (2R+60)$

Expanding the right side:

$R+60=1.4R+42$

Subtracting $R$ and $42$ from both sides:

$60-42=1.4R-R$

$18=0.4R$

Solving for $R$:

$R=\frac{18}{0.4}=45$

Now find Meera's score:

$M=45+60=105$

Thus, the marks scored by Rohan and Meera are 45 and 105, respectively.