The sum of two numbers is 125600. If one number is less than the other number by 14400, then value of the small number is:

Options

A. 70000
B. 84400
C. 55600
D. 62800

Answer

To solve the problem step by step, we will define the two numbers and set up equations based on the information given.

### Step 1: Define the Variables
Let the two numbers be \( x \) and \( y \), where \( x \) is the larger number and \( y \) is the smaller number.

### Step 2: Set Up the Equations
According to the problem:
1. The sum of the two numbers is \( 125600 \):
\[ x + y = 125600 \quad \text{(Equation 1)} \]
2. One number is less than the other by \( 14400 \):
\[ x - y = 14400 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
Now we will solve these two equations simultaneously. We can add Equation 1 and Equation 2 to eliminate \( y \).

Adding the two equations:
\[ (x + y) + (x - y) = 125600 + 14400 \]
This simplifies to:
\[ 2x = 140000 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{140000}{2} = 70000 \]

### Step 5: Substitute \( x \) to Find \( y \)
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ 70000 + y = 125600 \]
Subtract \( 70000 \) from both sides:
\[ y = 125600 - 70000 \]
\[ y = 55600 \]

### Conclusion
The value of the smaller number \( y \) is \( 55600 \).