The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is :

Options

A. 395
B. 380
C. 400
D. 425

Answer

To solve the problem, we need to find two numbers based on the information given. Let's denote the two numbers as \( x \) (the larger number) and \( y \) (the smaller number).

### Step 1: Set up the equations
From the problem, we have two pieces of information:
1. The product of the two numbers is 9375:
\[ x \cdot y = 9375 \]
2. The quotient when the larger number is divided by the smaller number is 15:
\[ \frac{x}{y} = 15 \]

### Step 2: Express \( x \) in terms of \( y \)
From the second equation, we can express \( x \) in terms of \( y \):
\[ x = 15y \]

### Step 3: Substitute \( x \) in the product equation
Now we can substitute \( x \) in the product equation:
\[ (15y) \cdot y = 9375 \]
This simplifies to:
\[ 15y^2 = 9375 \]

### Step 4: Solve for \( y^2 \)
To isolate \( y^2 \), divide both sides by 15:
\[ y^2 = \frac{9375}{15} \]

Calculating the right side:
\[ y^2 = 625 \]

### Step 5: Solve for \( y \)
Now, take the square root of both sides to find \( y \):
\[ y = \sqrt{625} = 25 \]

### Step 6: Find \( x \)
Now that we have \( y \), we can find \( x \) using the equation \( x = 15y \):
\[ x = 15 \cdot 25 = 375 \]

### Step 7: Calculate the sum of the numbers
Finally, we can find the sum of the two numbers:
\[ x + y = 375 + 25 = 400 \]

### Final Answer
The sum of the two numbers is \( 400 \).

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