Amar has some notes of Rs 10 and 20. The total number of notes are 70 and the total amount of money with him is Rs 1,050. Find the number of notes of 10 and 20 with him.

Options

A. 30 and 40
B. 35 and 35
C. 40 and 30
D. 45 and 25

Answer

To solve the problem, we will use algebraic equations. Let's break it down step by step.

### Step 1: Define the Variables
Let:
- \( x \) = number of Rs 10 notes
- \( y \) = number of Rs 20 notes

### Step 2: Set Up the Equations
From the problem, we know two things:
1. The total number of notes is 70:
\[ x + y = 70 \quad \text{(Equation 1)} \]
2. The total amount of money is Rs 1,050:
\[ 10x + 20y = 1050 \quad \text{(Equation 2)} \]

### Step 3: Solve Equation 1 for One Variable
We can express \( y \) in terms of \( x \) using Equation 1:
\[ y = 70 - x \quad \text{(Equation 3)} \]

### Step 4: Substitute Equation 3 into Equation 2
Now, substitute \( y \) from Equation 3 into Equation 2:
\[ 10x + 20(70 - x) = 1050 \]

### Step 5: Simplify the Equation
Distributing the 20:
\[ 10x + 1400 - 20x = 1050 \]
Combine like terms:
\[ -10x + 1400 = 1050 \]

### Step 6: Isolate \( x \)
Subtract 1400 from both sides:
\[ -10x = 1050 - 1400 \]
\[ -10x = -350 \]
Now, divide by -10:
\[ x = 35 \]

### Step 7: Find \( y \)
Now that we have \( x \), we can find \( y \) using Equation 3:
\[ y = 70 - x = 70 - 35 = 35 \]

### Conclusion
Thus, the number of Rs 10 notes is \( 35 \) and the number of Rs 20 notes is also \( 35 \).

### Final Answer
- Number of Rs 10 notes: **35**
- Number of Rs 20 notes: **35**