The LCM of two numbers is 12 times their HCF. The sum of the HCF and LCM is 403. If one of the number is 93, then the other is:

Options

A. 116
B. 124
C. 112
D. 120

Answer

To solve the problem step by step, we need to find the other number when we know one number (93), the relationship between LCM and HCF, and the sum of LCM and HCF.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
We know that the LCM of two numbers is 12 times their HCF. Let the HCF be denoted as \( h \). Therefore, we can express the LCM as:
\[ \text{LCM} = 12h \]

2. **Sum of LCM and HCF**:
According to the problem, the sum of the LCM and HCF is 403. We can write this as:
\[ h + \text{LCM} = 403 \]
Substituting the expression for LCM from the previous step:
\[ h + 12h = 403 \]
Simplifying this gives:
\[ 13h = 403 \]

3. **Finding HCF**:
Now we can solve for \( h \):
\[ h = \frac{403}{13} = 31 \]

4. **Finding LCM**:
Now that we have \( h \), we can find the LCM:
\[ \text{LCM} = 12h = 12 \times 31 = 372 \]

5. **Using the Relationship Between Numbers**:
Let the two numbers be \( a \) and \( b \). We know one number \( a = 93 \) and the relationship between LCM, HCF, and the two numbers:
\[ \text{LCM} = \frac{a \times b}{h} \]
Substituting the known values:
\[ 372 = \frac{93 \times b}{31} \]

6. **Solving for the Other Number**:
Rearranging the equation to solve for \( b \):
\[ 372 \times 31 = 93 \times b \]
\[ 11532 = 93b \]
\[ b = \frac{11532}{93} = 124 \]

### Final Answer:
The other number is **124**.