The LCM of two numbers is 44 times of their HCF. The sum of the LCM and HCF is 1125. If one number is 25, then the other number is:

Options

A. 1100
B. 975
C. 900
D. 800

Answer

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

### Step 1: Define the given information
We know that:
- The LCM (Least Common Multiple) of two numbers is 44 times their HCF (Highest Common Factor).
- The sum of the LCM and HCF is 1125.
- One of the numbers is 25.

### Step 2: Set up the equations
Let:
- HCF = x
- LCM = 44x (since LCM is 44 times HCF)

From the second piece of information, we can set up the equation:
\[ LCM + HCF = 1125 \]
Substituting the values we have:
\[ 44x + x = 1125 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 45x = 1125 \]

### Step 4: Solve for HCF (x)
To find x, divide both sides by 45:
\[ x = \frac{1125}{45} \]
Calculating this gives:
\[ x = 25 \]
So, the HCF is 25.

### Step 5: Find the LCM
Now, we can find the LCM using the value of HCF:
\[ LCM = 44x = 44 \times 25 = 1100 \]
So, the LCM is 1100.

### Step 6: Use the relationship between LCM, HCF, and the two numbers
We know that:
\[ LCM \times HCF = N1 \times N2 \]
Where N1 is 25 (the first number) and N2 is the second number we need to find. Substituting the known values:
\[ 1100 \times 25 = 25 \times N2 \]

### Step 7: Solve for N2
Now, we can solve for N2:
\[ 1100 \times 25 = 25 \times N2 \]
Dividing both sides by 25:
\[ N2 = \frac{1100 \times 25}{25} = 1100 \]

### Final Answer
The other number is **1100**.

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