The average marks obtained by A, B and C is 48. The average marks obtained by B and C is 52. The ratio of marks obtained by A to C is 4:3. Find the marks obtained by B.

The correct option is 74.

Step 1: Find the total marks obtained by A, B, and C.

We are given that the average marks obtained by A, B, and C is 48.

$\text{Average of A, B, C}=\frac{A+B+C}{3}=48$

Multiplying both sides by 3:

$A+B+C=48\times 3=144$    --- (Equation 1)

Step 2: Find the total marks obtained by B and C.

We are given that the average marks obtained by B and C is 52.

$\text{Average of B, C}=\frac{B+C}{2}=52$

Multiplying both sides by 2:

$B+C=52\times 2=104$    --- (Equation 2)

Step 3: Calculate the marks obtained by A.

Substitute Equation 2 into Equation 1:

$A+104=144$

$A=144-104=40$

Step 4: Find the marks obtained by C.

The ratio of marks obtained by A to C is given as 4 : 3.

$\frac{A}{C}=\frac{4}{3}$

Substitute $A=40$ into the ratio:

$\frac{40}{C}=\frac{4}{3}$

$C=\frac{40\times 3}{4}=30$

Step 5: Calculate the marks obtained by B.

Now, substitute $C=30$ into Equation 2 ($B+C=104$):

$B+30=104$

$B=104-30=74$

Thus, the marks obtained by B are 74.