I had Rs. 350 with me. I gave Rs. `((x)/(2) )` to Amit, Rs. `((x)/(3))` to Shreya and I am left with Rs. `((x)/(3))`. The amount I gave to Amit is _______.

Options

A. Rs. 150
B. Rs. 100
C. Rs. 250
D. Rs. 200

Answer

To solve the problem step by step, we will set up an equation based on the information given.

### Step 1: Set up the equation
We know that the total amount of money I had is Rs. 350. I gave Rs. \( \frac{x}{2} \) to Amit, Rs. \( \frac{x}{3} \) to Shreya, and I am left with Rs. \( \frac{x}{3} \).

So, we can write the equation:
\[ \frac{x}{2} + \frac{x}{3} + \frac{x}{3} = 350 \]

### Step 2: Simplify the equation
To solve this equation, we need to find a common denominator for the fractions. The least common multiple (LCM) of 2 and 3 is 6.

Rewriting the equation with a common denominator:
\[ \frac{3x}{6} + \frac{2x}{6} + \frac{2x}{6} = 350 \]

### Step 3: Combine the fractions
Now, we can combine the fractions on the left side:
\[ \frac{3x + 2x + 2x}{6} = 350 \]
This simplifies to:
\[ \frac{7x}{6} = 350 \]

### Step 4: Solve for \( x \)
To isolate \( x \), we can multiply both sides of the equation by 6:
\[ 7x = 350 \times 6 \]
Calculating the right side:
\[ 7x = 2100 \]
Now, divide both sides by 7:
\[ x = \frac{2100}{7} = 300 \]

### Step 5: Find the amount given to Amit
We need to find the amount given to Amit, which is \( \frac{x}{2} \):
\[ \text{Amount given to Amit} = \frac{300}{2} = 150 \]

### Final Answer
The amount I gave to Amit is **Rs. 150**.

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