A year ago Akash’s father’s age was 9 times that of Akash. After 3 years his father's age will be 5 times that of his age. How old will Akash be next year?

Options

A. 4 years
B. 5 years
C. 8 years
D. 6 years

Answer

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

### Step 1: Define Variables
Let Akash's age a year ago be \( x \). Therefore, Akash's father's age a year ago will be \( 9x \) (since it is given that Akash's father's age was 9 times that of Akash).

### Step 2: Present Ages
Now, we can express their present ages:
- Akash's present age = \( x + 1 \)
- Father's present age = \( 9x + 1 \)

### Step 3: Future Ages
According to the problem, after 3 years:
- Akash's age will be \( (x + 1) + 3 = x + 4 \)
- Father's age will be \( (9x + 1) + 3 = 9x + 4 \)

### Step 4: Set Up the Equation
We are given that after 3 years, the father's age will be 5 times Akash's age. Therefore, we can set up the equation:
\[ 9x + 4 = 5(x + 4) \]

### Step 5: Simplify the Equation
Expanding the right side of the equation:
\[ 9x + 4 = 5x + 20 \]

### Step 6: Solve for \( x \)
Now, we will isolate \( x \):
\[ 9x - 5x = 20 - 4 \]
\[ 4x = 16 \]
\[ x = 4 \]

### Step 7: Find Present Age of Akash
Now that we have \( x \), we can find Akash's present age:
\[ \text{Present age of Akash} = x + 1 = 4 + 1 = 5 \]

### Step 8: Find Akash's Age Next Year
To find Akash's age next year:
\[ \text{Akash's age next year} = 5 + 1 = 6 \]

### Conclusion
Akash will be **6 years old next year**.

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