Jeevesh had 92 currency notes in all, some of which were of Rs 100 denomination and the remaining of Rs 50 denominator. The total value of amount of all these currency notes was Rs 6350. How much amount in rupees did he have in the denomination of Rs 50 ?

Options

A. 3500
B. 3350
C. 2850
D. 2600

Explanation

To solve the problem, we will define variables and set up equations based on the information provided.

### Step 1: Define Variables
Let:
- \( x \) = number of Rs. 100 notes
- \( y \) = number of Rs. 50 notes

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of notes is 92:
\[ x + y = 92 \quad \text{(1)} \]
2. The total value of the notes is Rs. 6350:
\[ 100x + 50y = 6350 \quad \text{(2)} \]

### Step 3: Solve the First Equation for One Variable
From equation (1), we can express \( y \) in terms of \( x \):
\[ y = 92 - x \quad \text{(3)} \]

### Step 4: Substitute into the Second Equation
Now, substitute equation (3) into equation (2):
\[ 100x + 50(92 - x) = 6350 \]

### Step 5: Simplify the Equation
Distributing the 50:
\[ 100x + 4600 - 50x = 6350 \]
Combine like terms:
\[ 50x + 4600 = 6350 \]

### Step 6: Isolate the Variable
Subtract 4600 from both sides:
\[ 50x = 6350 - 4600 \]
\[ 50x = 1750 \]

### Step 7: Solve for \( x \)
Divide both sides by 50:
\[ x = \frac{1750}{50} = 35 \]

### Step 8: Find \( y \)
Now substitute \( x = 35 \) back into equation (3):
\[ y = 92 - 35 = 57 \]

### Step 9: Calculate the Total Amount in Rs. 50 Notes
The total amount in Rs. 50 notes is:
\[ \text{Total amount in Rs. 50 notes} = 50y = 50 \times 57 = 2850 \]

### Final Answer
Jeevesh had Rs. 2850 in the denomination of Rs. 50.

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