The total of the present ages of A,B,C and D is 96 years. What is B's present age ?
(i) The average age of A, B and D is 20 years.
(ii) The average age of C and D is 25 years.

Answer

To solve the problem of finding B's present age given the total ages of A, B, C, and D, we will analyze the provided statements step by step.

### Given:
- Total age of A, B, C, and D = 96 years.

### Step 1: Analyze Statement (i)
**Statement (i)**: The average age of A, B, and D is 20 years.

Using the formula for average:
\[ \text{Average} = \frac{\text{Sum of ages}}{\text{Number of people}} \]
We can express this as:
\[ 20 = \frac{A + B + D}{3} \]
Multiplying both sides by 3 gives:
\[ A + B + D = 60 \]

### Step 2: Substitute into the total age equation
Now, we know:
\[ A + B + C + D = 96 \]
Substituting \(A + B + D = 60\) into the total age equation:
\[ 60 + C = 96 \]
This leads to:
\[ C = 96 - 60 = 36 \]

### Step 3: Analyze what we have
At this point, we have the age of C, but we still do not have enough information to find B's age directly because we do not have the individual ages of A, B, or D.

### Conclusion for Statement (i)
Thus, **Statement (i) alone is not sufficient** to determine B's age.

### Step 4: Analyze Statement (ii)
**Statement (ii)**: The average age of C and D is 25 years.

Using the average formula again:
\[ 25 = \frac{C + D}{2} \]
Multiplying both sides by 2 gives:
\[ C + D = 50 \]

### Step 5: Substitute into the total age equation
Now, substituting \(C + D = 50\) into the total age equation:
\[ A + B + C + D = 96 \]
This gives us:
\[ A + B + 50 = 96 \]
From this, we can find:
\[ A + B = 96 - 50 = 46 \]

### Step 6: Analyze what we have
At this point, we have the sum of A and B's ages, but we still do not have enough information to find B's age directly because we do not know the individual ages of A or B.

### Conclusion for Statement (ii)
Thus, **Statement (ii) alone is also not sufficient** to determine B's age.

### Final Conclusion
Since neither statement alone is sufficient to find B's present age, we conclude that both statements together are also not sufficient to determine B's age.

### Final Answer:
Both statements are not sufficient to determine B's present age.

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