The ratio of marks of A and B is 3 : 4 and the ratio of marks of B and C is 4 : 5. If the difference in the marks of C and A is 30, then how much marks does B get?

The correct answer is 60.

Step-by-Step Explanation:

1. Understand the Given Ratios:
We are given two ratios:
The ratio of marks of A and B is $A:B=3:4$.
The ratio of marks of B and C is $B:C=4:5$.

2. Combine the Ratios:
Since the term for B is identical in both ratios (which is 4 parts), we can write the combined ratio of marks for A, B, and C directly:
$A:B:C=3:4:5$

3. Formulate Equations using a Common Constant:
Let the marks obtained by A, B, and C be $3x$, $4x$, and $5x$ respectively, where $x$ is a constant.

4. Use the Given Difference to Solve for $x$:
We are given that the difference in the marks of C and A is 30.
Therefore, we can write:
$C-A=30$
Substituting the values in terms of $x$:
$5x-3x=30$
$2x=30$
$x=15$

5. Calculate the Marks obtained by B:
B's marks are given by:
$B=4x$
Substituting the value of $x=15$:
$B=4\times 15=60$

Thus, B gets 60 marks.