A has certain amount in his account. He gives half of this to his eldest son and one third of the remaining to his youngest son. The amount with him now is :

Options

A. `1/3` of the original
B. `2/3` of the original
C. `3/4` of the original
D. `1/6` of the original

Answer

To solve the problem step by step, we will denote the initial amount A has in his account as \( x \).

### Step 1: Determine the amount given to the eldest son
A gives half of his total amount \( x \) to his eldest son. Therefore, the amount given to the eldest son is:
\[ \text{Amount given to eldest son} = \frac{x}{2} \]

### Step 2: Calculate the remaining amount after giving to the eldest son
After giving half of his amount to the eldest son, the remaining amount in A's account is:
\[ \text{Remaining amount} = x - \frac{x}{2} = \frac{x}{2} \]

### Step 3: Determine the amount given to the youngest son
A then gives one third of the remaining amount to his youngest son. The remaining amount is \( \frac{x}{2} \), so the amount given to the youngest son is:
\[ \text{Amount given to youngest son} = \frac{1}{3} \times \frac{x}{2} = \frac{x}{6} \]

### Step 4: Calculate the final amount with A
Now, we need to find out how much money A has left after giving money to both sons. The final amount A has is:
\[ \text{Final amount} = \text{Remaining amount} - \text{Amount given to youngest son} \]
Substituting the values we have:
\[ \text{Final amount} = \frac{x}{2} - \frac{x}{6} \]

### Step 5: Simplify the final amount
To subtract these fractions, we need a common denominator. The least common multiple of 2 and 6 is 6. Thus, we convert \( \frac{x}{2} \) to have a denominator of 6:
\[ \frac{x}{2} = \frac{3x}{6} \]
Now we can perform the subtraction:
\[ \text{Final amount} = \frac{3x}{6} - \frac{x}{6} = \frac{3x - x}{6} = \frac{2x}{6} = \frac{x}{3} \]

### Conclusion
The amount A has now in his account is:
\[ \frac{x}{3} \]