The price of 8 book and 24 registers is Rs 1760. If the price of one book is Rs 124 more than the price of one register, what is the total price of 4 books and 2 registers ?

Options

A. 512
B. 674
C. 456
D. 640

Answer

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

### Step 1: Define the Variables
Let:
- \( x \) = price of one book
- \( y \) = price of one register

### Step 2: Set Up the Equations
From the problem, we have two pieces of information:
1. The price of 8 books and 24 registers is Rs 1760.
\[ 8x + 24y = 1760 \quad \text{(Equation 1)} \]
2. The price of one book is Rs 124 more than the price of one register.
\[ x = y + 124 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1
We will substitute \( x \) from Equation 2 into Equation 1:
\[ 8(y + 124) + 24y = 1760 \]

### Step 4: Simplify the Equation
Distributing the 8:
\[ 8y + 992 + 24y = 1760 \]
Combine like terms:
\[ 32y + 992 = 1760 \]

### Step 5: Solve for \( y \)
Subtract 992 from both sides:
\[ 32y = 1760 - 992 \]
\[ 32y = 768 \]
Now, divide by 32:
\[ y = \frac{768}{32} = 24 \]

### Step 6: Find the Price of One Book
Now that we have \( y \), we can find \( x \):
\[ x = y + 124 = 24 + 124 = 148 \]

### Step 7: Calculate the Total Price of 4 Books and 2 Registers
Now we need to calculate the total price for 4 books and 2 registers:
\[ \text{Total Price} = 4x + 2y = 4(148) + 2(24) \]
Calculating each term:
\[ 4(148) = 592 \]
\[ 2(24) = 48 \]
Adding these together:
\[ \text{Total Price} = 592 + 48 = 640 \]

### Final Answer
The total price of 4 books and 2 registers is Rs 640.