To find out how much the marks increased after rechecking, we can calculate the new score based on 75% of the total marks and subtract the original score from it.

1. Total Marks = 60
2. Original Marks = 42
3. New Marks (after rechecking) = $75\%$ of 60

$\text{New Marks} = \frac{75}{100} \times 60 = 45$

4. Increase in Marks = New Marks - Original Marks

$\text{Increase} = 45 - 42 = 3$

So, the marks increased by 3 after rechecking.

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What percentage did the student originally score before rechecking?
2. How would the increase in marks change if the total was 80 instead of 60?
3. If the student had originally scored 30, how much would the marks increase after rechecking?
4. What if the rechecked score was 80% instead of 75%, how much would the marks increase?
5. How do we calculate the percentage increase in marks after rechecking?

Tip: Always check your percentages by recalculating based on the total marks to ensure accurate results.