In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to thrice of remainder. Find the dividend.

Answer

To solve the problem step by step, let's define the variables based on the information provided:

1. **Given Information:**
- Remainder (R) = 6
- Divisor (D) = 5 times the Quotient (Q)
- Divisor (D) is also obtained by adding 2 to thrice the remainder.

2. **Step 1: Find the Divisor (D)**
- According to the problem, the divisor is obtained by adding 2 to thrice the remainder.
- So, we can express this mathematically as:
\[ D = 3R + 2 \]
- Substituting the value of the remainder (R = 6):
\[ D = 3 \times 6 + 2 = 18 + 2 = 20 \]

3. **Step 2: Find the Quotient (Q)**
- We know that the divisor is 5 times the quotient:
\[ D = 5Q \]
- We can rearrange this to find the quotient:
\[ Q = \frac{D}{5} \]
- Substituting the value of the divisor (D = 20):
\[ Q = \frac{20}{5} = 4 \]

4. **Step 3: Find the Dividend (N)**
- The dividend can be calculated using the formula:
\[ N = D \times Q + R \]
- Substituting the values we have:
\[ N = 20 \times 4 + 6 = 80 + 6 = 86 \]

5. **Final Answer:**
- The dividend is **86**.