A bill for Rs. 40 is paid by means of Rs. 5 notes and Rs. 10 notes. Seven notes are used in all. If x is the number of Rs. 5 notes and y is the number of Rs. 10 notes then

Options

A. `x+y=7` and `x+2y=40`
B. `x+y=7` and `x+2y=8`
C. `x+y=7` and `2x+y=8`
D. `x+y=7` and `2x+y=40`

Answer

To solve the problem, we need to set up a system of equations based on the information given.

### Step 1: Define the 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 used is 7.
2. The total amount paid is Rs. 40.

From the first piece of information, we can write the equation:
\[ x + y = 7 \]
(Equation 1)

From the second piece of information, we can write the equation based on the total value of the notes:
\[ 5x + 10y = 40 \]
(Equation 2)

### Step 3: Simplify the Second Equation
We can simplify Equation 2 by dividing all terms by 5:
\[ x + 2y = 8 \]
(Equation 3)

### Step 4: Solve the System of Equations
Now we have a system of two equations:
1. \( x + y = 7 \) (Equation 1)
2. \( x + 2y = 8 \) (Equation 3)

We can solve these equations using substitution or elimination. Here, we will use substitution.

From Equation 1, we can express \( x \) in terms of \( y \):
\[ x = 7 - y \]

Now, substitute this expression for \( x \) into Equation 3:
\[ (7 - y) + 2y = 8 \]

### Step 5: Simplify and Solve for \( y \)
Now simplify the equation:
\[ 7 - y + 2y = 8 \]
\[ 7 + y = 8 \]
Subtract 7 from both sides:
\[ y = 1 \]

### Step 6: Substitute Back to Find \( x \)
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ x + 1 = 7 \]
Subtract 1 from both sides:
\[ x = 6 \]

### Step 7: Conclusion
Thus, the solution is:
- Number of Rs. 5 notes (x) = 6
- Number of Rs. 10 notes (y) = 1

### Final Answer
The number of Rs. 5 notes is 6 and the number of Rs. 10 notes is 1.

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