Rs. 200 was distributed among three persons - Anil. Binay and Chinmay. Binay received 50% more than Chinmay. Anil received Rs. 10 more than 150% of what Binay received. How much money did Anil receive?

Options

A. Rs 40
B. Rs 60
C. Rs 43
D. Rs 100

Answer

To solve the problem step by step, let's denote the amount Chinmay receives as \( x \).

### Step 1: Define the amounts for each person
- Let Chinmay receive \( x \).
- Binay receives 50% more than Chinmay, which can be calculated as:
\[ \text{Binay's amount} = x + 0.5x = 1.5x \]

### Step 2: Calculate Anil's amount
- Anil receives Rs. 10 more than 150% of what Binay received. First, we calculate 150% of Binay's amount:
\[ 150\% \text{ of Binay's amount} = 1.5 \times (1.5x) = 2.25x \]
- Therefore, Anil's amount can be expressed as:
\[ \text{Anil's amount} = 2.25x + 10 \]

### Step 3: Set up the equation for the total amount
- The total amount distributed among Anil, Binay, and Chinmay is Rs. 200. Therefore, we can write the equation:
\[ x + 1.5x + (2.25x + 10) = 200 \]

### Step 4: Simplify the equation
- Combine like terms:
\[ x + 1.5x + 2.25x + 10 = 200 \]
\[ 4.75x + 10 = 200 \]

### Step 5: Solve for \( x \)
- Subtract 10 from both sides:
\[ 4.75x = 190 \]
- Now, divide both sides by 4.75 to find \( x \):
\[ x = \frac{190}{4.75} = 40 \]

### Step 6: Calculate Anil's amount
- Now that we have \( x = 40 \), we can substitute this value back into the equation for Anil's amount:
\[ \text{Anil's amount} = 2.25 \times 40 + 10 \]
\[ = 90 + 10 = 100 \]

### Final Answer
- Anil received Rs. 100.

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