The difference between two numbers is 1375. On dividing larger number by the smaller number, the quotient is 6 and the remainder is 25. Find the smaller number.

Options

A. 250
B. 270
C. 275
D. 300

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Define the Variables
Let the smaller number be \( S \) and the larger number be \( L \).

### Step 2: Set Up the Equations
From the problem, we know two things:
1. The difference between the two numbers is 1375:
\[ L - S = 1375 \quad \text{(Equation 1)} \]
2. When the larger number is divided by the smaller number, the quotient is 6 and the remainder is 25. This can be expressed as:
\[ L = 6S + 25 \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 1 into Equation 2
From Equation 1, we can express \( L \) in terms of \( S \):
\[ L = S + 1375 \]
Now, substitute this expression for \( L \) into Equation 2:
\[ S + 1375 = 6S + 25 \]

### Step 4: Rearrange the Equation
Now, rearranging the equation gives:
\[ 1375 - 25 = 6S - S \]
This simplifies to:
\[ 1350 = 5S \]

### Step 5: Solve for \( S \)
Now, divide both sides by 5 to find \( S \):
\[ S = \frac{1350}{5} = 270 \]

### Step 6: Conclusion
Thus, the smaller number \( S \) is:
\[ \boxed{270} \]

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