In finding the HCF of two numbers by division method four successive quotient are 4,3,6 and 5 respectively. and final divisor is 12. What are two numbers?

Options

A. 1126, 5376
B. 1116, 4836
C. 1056, 4596
D. 1176, 5076

Answer

To find the two numbers given the HCF and the successive quotients, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem:**
We know that the HCF of two numbers is found using the division method, where we have four successive quotients (4, 3, 6, and 5) and the final divisor (12).

2. **Using the Division Method:**
We can represent the process of finding the HCF as follows:
- Let the two numbers be \( a \) and \( b \) (with \( a < b \)).
- The division steps can be represented as:
- \( b = a \times 4 + r_1 \)
- \( a = r_1 \times 3 + r_2 \)
- \( r_1 = r_2 \times 6 + r_3 \)
- \( r_2 = r_3 \times 5 + 12 \)

3. **Calculating the First Number:**
- From the last equation, where the final divisor is 12:
\[ r_2 = 12 \times 5 + r_3 \]
Since \( r_3 = 0 \) (as it is the last remainder), we calculate:
\[ r_2 = 12 \times 5 = 60 \]

4. **Calculating the Second Number:**
- Now, using \( r_1 \):
\[ a = r_1 \times 3 + r_2 \]
We know \( r_2 = 60 \):
\[ r_1 = 60 \times 6 + r_3 \]
Again, since \( r_3 = 0 \):
\[ r_1 = 60 \times 6 = 360 \]

5. **Finding the First Number:**
- Now, substituting back to find \( b \):
\[ b = a \times 4 + r_1 \]
We know \( r_1 = 360 \):
\[ a = 360 \times 3 + 60 = 1080 + 60 = 1140 \]

6. **Final Calculation:**
- Finally, we can find the two numbers:
- First number \( a = 1140 \)
- Second number \( b = 360 \times 4 + 12 = 1440 + 12 = 1452 \)

### Conclusion:
The two numbers are **1140** and **1452**.