Five years ago, the ratio of the age of A to that of B was 3:2. C is 7 years younger than A. The present age of C is 2 times of D's present age. What is the present age of B, if the age of D after 6 years is 35 years?

Options

A. 40 years
B. 42 years
C. 45 years
D. 38 years

Answer

To solve the problem step by step, we will define the ages based on the given information and use algebra to find the present age of B.

### Step 1: Define the ages 5 years ago
Let the age of A 5 years ago be \(3x\) and the age of B 5 years ago be \(2x\). This is based on the ratio of their ages given as 3:2.

### Step 2: Calculate present ages of A and B
Since these ages are from 5 years ago, we can express their present ages:
- Present age of A = \(3x + 5\)
- Present age of B = \(2x + 5\)

### Step 3: Determine the age of C
We know that C is 7 years younger than A. Thus, we can express C's present age as:
- Present age of C = \( (3x + 5) - 7 = 3x - 2\)

### Step 4: Relate C's age to D's age
We are told that the present age of C is twice the present age of D. Let D's present age be \(y\). Therefore, we can write:
- \(3x - 2 = 2y\)

### Step 5: Find D's present age
We know that D's age after 6 years will be 35 years. Thus, we can express D's current age as:
- \(y + 6 = 35\)
- Solving for \(y\), we get \(y = 35 - 6 = 29\).

### Step 6: Substitute D's age into the equation
Now we substitute \(y = 29\) into the equation for C's age:
- \(3x - 2 = 2(29)\)
- \(3x - 2 = 58\)

### Step 7: Solve for \(x\)
Now, we solve for \(x\):
- \(3x = 58 + 2\)
- \(3x = 60\)
- \(x = 20\)

### Step 8: Calculate the present age of B
Now that we have \(x\), we can find the present age of B:
- Present age of B = \(2x + 5 = 2(20) + 5 = 40 + 5 = 45\).

### Conclusion
Thus, the present age of B is **45 years**.

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