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.

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**Solution:**

1. Let the marks obtained by A, B, and C be *A*, *B*, and *C* respectively.

2. Given the average marks of A, B, and C is 48, so:
   $$\frac{A + B + C}{3} = 48 \implies A + B + C = 144$$

3. The average marks of B and C is 52, so:
   $$\frac{B + C}{2} = 52 \implies B + C = 104$$

4. From the above two equations:
   $$A + B + C = 144$$
   $$B + C = 104$$

Subtracting the second from the first:
   $$A = 144 - 104 = 40$$

5. The ratio of marks obtained by A to C is 4:3, so:
   $$\frac{A}{C} = \frac{4}{3} \implies A = \frac{4}{3}C$$

6. Substitute *A = 40* from step 4 into the ratio equation:
   $$40 = \frac{4}{3}C \implies C = \frac{40 	imes 3}{4} = 30$$

7. Since *B + C = 104*, and *C = 30*, then:
   $$B = 104 - 30 = 74$$

**Answer:** $74$

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