In finding the HCF of two numbersby division method, the quotients are 1, 8 and 2 respectively, and the last divisor is 105. What is the sum of the numbers?

Options

A. 3570
B. 3885
C. 3780
D. 3675

Answer

To find the sum of the two numbers using the given information, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Division Method**:
In the division method for finding the HCF, we have two numbers, and we repeatedly divide the larger number by the smaller number until we reach a remainder of 0. The last non-zero remainder is the HCF.

2. **Given Information**:
We know the quotients from the division are 1, 8, and 2, and the last divisor is 105.

3. **Setting Up the Equations**:
- For the last step, we have:
\[ \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \]
Since the last divisor is 105 and the quotient is 2, and the remainder is 0, we can write:
\[ \text{Dividend} = 105 \times 2 + 0 = 210 \]

4. **Next Step**:
- Now, we take the dividend 210 and the next quotient, which is 8. The last divisor (which is now the new divisor) is 210, and we need to find the next dividend:
\[ \text{Dividend} = 210 \times 8 + 105 \]
\[ = 1680 + 105 = 1785 \]

5. **Final Step**:
- Now, we take the last dividend 1785 and the next quotient, which is 1:
\[ \text{Dividend} = 1785 \times 1 + 210 \]
\[ = 1785 + 210 = 1995 \]

6. **Identifying the Two Numbers**:
- The two numbers we have found are 1785 and 1995.

7. **Calculating the Sum**:
- Finally, we calculate the sum of these two numbers:
\[ \text{Sum} = 1785 + 1995 = 3780 \]

### Final Answer:
The sum of the two numbers is **3780**.

---