Ram's income is ₹100 more than that of Shyam. If the average income of Ram and Shyam is ₹ 850, then Ram's income is :

Options

A. ₹ 900
B. ₹ 800
C. ₹ 850
D. ₹ 475

Answer

To solve the problem step by step, let's denote Ram's income as \( R \) and Shyam's income as \( S \).

### Step 1: Set up the equations based on the information given.
From the problem, we know:
1. Ram's income is ₹100 more than Shyam's income:
\[ R = S + 100 \]
2. The average income of Ram and Shyam is ₹850:
\[ \frac{R + S}{2} = 850 \]

### Step 2: Solve the average income equation.
To eliminate the fraction, we can multiply both sides of the average income equation by 2:
\[ R + S = 1700 \]

### Step 3: Substitute Ram's income in the average equation.
Now, we can substitute the expression for \( R \) from the first equation into the second equation:
\[ (S + 100) + S = 1700 \]

### Step 4: Simplify the equation.
Combine like terms:
\[ 2S + 100 = 1700 \]

### Step 5: Isolate Shyam's income.
Subtract 100 from both sides:
\[ 2S = 1600 \]

Now, divide by 2:
\[ S = 800 \]

### Step 6: Find Ram's income.
Now that we have Shyam's income, we can find Ram's income using the first equation:
\[ R = S + 100 = 800 + 100 = 900 \]

### Conclusion:
Thus, Ram's income is ₹900.