Rakesh's monthly income is 2.5 times Gagan's monthly income. Gagan's monthly income is 15% less than Prabhat's monthly income. If difference between 20% of Rakesh monthly income and 5% of Prabhat's monthly income is 7500 Rs. Then, find the monthly income of Gagan.

Options

A. 18000
B. 19000
C. 20000
D. 17000

Answer

To solve the problem step by step, we will break down the information provided and use algebra to find Gagan's monthly income.

### Step 1: Define the Variables
Let:
- Gagan's monthly income = G
- Prabhat's monthly income = P
- Rakesh's monthly income = R

### Step 2: Set Up the Relationships
From the problem, we know:
1. Rakesh's monthly income is 2.5 times Gagan's monthly income:
\[ R = 2.5G \]
2. Gagan's monthly income is 15% less than Prabhat's monthly income:
\[ G = P - 0.15P = 0.85P \]

### Step 3: Substitute G in terms of P into R
Now, substitute \( G \) in the equation for \( R \):
\[ R = 2.5(0.85P) = 2.125P \]

### Step 4: Set Up the Equation from the Given Condition
We are given that the difference between 20% of Rakesh's monthly income and 5% of Prabhat's monthly income is Rs. 7500:
\[ 0.20R - 0.05P = 7500 \]
Substituting \( R \) from the previous step:
\[ 0.20(2.125P) - 0.05P = 7500 \]

### Step 5: Simplify the Equation
Now, simplify the equation:
\[ 0.425P - 0.05P = 7500 \]
\[ 0.375P = 7500 \]

### Step 6: Solve for P
To find \( P \), divide both sides by 0.375:
\[ P = \frac{7500}{0.375} = 20000 \]

### Step 7: Find Gagan's Monthly Income
Now that we have \( P \), we can find \( G \):
\[ G = 0.85P = 0.85 \times 20000 = 17000 \]

### Final Answer
Thus, Gagan's monthly income is **Rs. 17000**.

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