Mini is 6 years younger than P and also Mini is 6 years older than Q. Twelve years hence the respective ratio between the ages of P and Q at that time will be `4:3`. What is the sum of present ages of P and Q ? (in years)

Options

A. 42
B. 48
C. 64
D. 60

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Variables
Let the present age of P be \( P \) years.
Since Mini is 6 years younger than P, Mini's age will be \( P - 6 \) years.
Since Mini is also 6 years older than Q, we can express Q's age as \( (P - 6) - 6 = P - 12 \) years.

### Step 2: Set Up the Age After 12 Years
In 12 years, the ages of P and Q will be:
- Age of P after 12 years: \( P + 12 \)
- Age of Q after 12 years: \( (P - 12) + 12 = P \)

### Step 3: Set Up the Ratio
According to the problem, the ratio of the ages of P and Q after 12 years is \( 4:3 \). Therefore, we can set up the equation:
\[ \frac{P + 12}{P} = \frac{4}{3} \]

### Step 4: Cross-Multiply to Solve for P
Cross-multiplying gives us:
\[ 3(P + 12) = 4P \]
Expanding this, we have:
\[ 3P + 36 = 4P \]

### Step 5: Rearrange to Isolate P
Rearranging the equation to isolate \( P \):
\[ 36 = 4P - 3P \]
\[ 36 = P \]

### Step 6: Find Q's Age
Now that we have \( P = 36 \), we can find Q's age:
\[ Q = P - 12 = 36 - 12 = 24 \]

### Step 7: Calculate the Sum of Present Ages
Finally, we calculate the sum of the present ages of P and Q:
\[ P + Q = 36 + 24 = 60 \]

### Final Answer
The sum of the present ages of P and Q is **60 years**.

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