A and B are friends. A is elderto B by 5 years. B's sister C is half the age of B while A's father D is 8 years older than twice the age of B. If the present age of B. If the present age of D is 48 years, then find the present ages of A, B and C respectively.

Options

A. 50 years, 25 years, 20 years
B. 40 years, 20 years, 15 years
C. 20 years, 15 years, 10 years
D. 25 years, 20 years, 10 years

Answer

To solve the problem step by step, we will define the ages of A, B, C, and D using algebraic expressions based on the information provided in the question.

### Step 1: Define the variables
Let the present age of B be \( B \).
Since A is elder to B by 5 years, we can express A's age as:
\[ A = B + 5 \]

### Step 2: Define C's age
B's sister C is half the age of B, so we can express C's age as:
\[ C = \frac{B}{2} \]

### Step 3: Define D's age
According to the problem, A's father D is 8 years older than twice the age of B. Therefore, we can express D's age as:
\[ D = 2B + 8 \]

### Step 4: Set up the equation using D's age
We are given that the present age of D is 48 years. Thus, we can set up the equation:
\[ 2B + 8 = 48 \]

### Step 5: Solve for B
Now, we will solve for B:
1. Subtract 8 from both sides:
\[ 2B = 48 - 8 \]
\[ 2B = 40 \]
2. Divide both sides by 2:
\[ B = \frac{40}{2} \]
\[ B = 20 \]

### Step 6: Calculate A's age
Now that we have B's age, we can find A's age:
\[ A = B + 5 = 20 + 5 = 25 \]

### Step 7: Calculate C's age
Now we can find C's age:
\[ C = \frac{B}{2} = \frac{20}{2} = 10 \]

### Step 8: Present ages
Thus, the present ages are:
- A's age = 25 years
- B's age = 20 years
- C's age = 10 years

### Final Answer
The present ages of A, B, and C are 25 years, 20 years, and 10 years respectively.

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