A man went to a Bank with Rs. 1000. He asked the cashier to give him Rs. 5 and Rs. 10 notes only in return. The man got 175 notes in all. Find how many notes of Rs. 5 and Rs. 10 did he receive.

Answer

To solve the problem step by step, we will define variables, set up equations based on the information given, and then solve those equations.

### Step 1: Define Variables
Let:
- \( x \) = number of Rs. 5 notes
- \( y \) = number of Rs. 10 notes

### Step 2: Set Up the Equations
From the problem, we have two pieces of information:
1. The total number of notes is 175.
2. The total amount of money is Rs. 1000.

From the first piece of information, we can write the equation:
\[ x + y = 175 \quad \text{(Equation 1)} \]

From the second piece of information, we can write the equation based on the value of the notes:
\[ 5x + 10y = 1000 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing all terms by 5:
\[ x + 2y = 200 \quad \text{(Equation 3)} \]

### Step 4: Solve the Equations
Now we have two equations:
1. \( x + y = 175 \) (Equation 1)
2. \( x + 2y = 200 \) (Equation 3)

We can solve these equations using substitution or elimination. Let's use substitution.

From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 175 - y \]

Now, substitute this value of \( x \) into Equation 3:
\[ (175 - y) + 2y = 200 \]
\[ 175 + y = 200 \]
\[ y = 200 - 175 \]
\[ y = 25 \]

### Step 5: Find the Value of \( x \)
Now that we have \( y \), we can find \( x \):
\[ x = 175 - y \]
\[ x = 175 - 25 \]
\[ x = 150 \]

### Conclusion
The man received:
- **150 notes of Rs. 5**
- **25 notes of Rs. 10**