Deepak is 4 times as old as his son. Four years hence the sum of their ages will be 43 years. How old is Deepak’s son now ?

Options

A. 5 years
B. 7 years
C. 8 years
D. 10 years

Answer

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

### Step 1: Define Variables
Let:
- \( Y \) = age of Deepak's son
- \( X \) = age of Deepak

### Step 2: Set Up the First Equation
According to the problem, Deepak is 4 times as old as his son. Therefore, we can write the first equation as:
\[ X = 4Y \]

### Step 3: Set Up the Second Equation
The problem states that four years from now, the sum of their ages will be 43 years. In four years, Deepak's age will be \( X + 4 \) and his son's age will be \( Y + 4 \). Thus, we can write the second equation as:
\[ (X + 4) + (Y + 4) = 43 \]
This simplifies to:
\[ X + Y + 8 = 43 \]
So, we can rearrange it to:
\[ X + Y = 35 \]

### Step 4: Substitute the First Equation into the Second Equation
Now, we can substitute the value of \( X \) from the first equation into the second equation:
\[ 4Y + Y = 35 \]
This simplifies to:
\[ 5Y = 35 \]

### Step 5: Solve for \( Y \)
To find the age of Deepak's son, divide both sides of the equation by 5:
\[ Y = \frac{35}{5} \]
Thus:
\[ Y = 7 \]

### Conclusion
Deepak's son is currently **7 years old**.

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