A sum of ₹12,500 is distributed among A, B, C and D such that A gets ₹800 more than what B gets, C gets twice of what B gets and D gets ₹900 more than what A gets. The ratio in which D, C, B and A receive the sums is:

Options

A. 28 : 40 : 20 : 37
B. 28 : 20 : 40 : 37
C. 37 : 20 : 40 : 28
D. 37 : 40 : 20 : 28

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define Variables
Let the amount received by B be \( x \).

### Step 2: Express Amounts for A, C, and D
- According to the question, A receives ₹800 more than B:
\[ A = x + 800 \]
- C receives twice what B gets:
\[ C = 2x \]
- D receives ₹900 more than A:
\[ D = (x + 800) + 900 = x + 1700 \]

### Step 3: Set Up the Equation
The total amount distributed among A, B, C, and D is ₹12,500. Therefore, we can set up the equation:
\[ A + B + C + D = 12500 \]
Substituting the expressions we found:
\[ (x + 800) + x + (2x) + (x + 1700) = 12500 \]

### Step 4: Simplify the Equation
Combine like terms:
\[ 5x + 800 + 1700 = 12500 \]
This simplifies to:
\[ 5x + 2500 = 12500 \]

### Step 5: Solve for \( x \)
Subtract 2500 from both sides:
\[ 5x = 12500 - 2500 \]
\[ 5x = 10000 \]
Now, divide by 5:
\[ x = \frac{10000}{5} = 2000 \]

### Step 6: Calculate Amounts for A, C, and D
Now that we have \( x \), we can find the amounts for A, C, and D:
- Amount for B:
\[ B = x = 2000 \]
- Amount for A:
\[ A = x + 800 = 2000 + 800 = 2800 \]
- Amount for C:
\[ C = 2x = 2 \times 2000 = 4000 \]
- Amount for D:
\[ D = x + 1700 = 2000 + 1700 = 3700 \]

### Step 7: Write the Ratio
Now we have:
- D = 3700
- C = 4000
- B = 2000
- A = 2800

The ratio of D : C : B : A is:
\[ 3700 : 4000 : 2000 : 2800 \]

### Step 8: Simplify the Ratio
To simplify the ratio, we can divide each term by 100:
\[ 37 : 40 : 20 : 28 \]

### Final Answer
The ratio in which D, C, B, and A receive the sums is:
\[ \text{D : C : B : A} = 37 : 40 : 20 : 28 \]

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