If a number is divided by 129 leaves remainder 27 if 4 times of this number is divided by 86 then what will be the remainder?

Options

A. 19
B. 22
C. 23
D. 25

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Define the number
Let the number be \( n \). According to the problem, when \( n \) is divided by 129, it leaves a remainder of 27. This can be expressed mathematically as:
\[ n = 129k + 27 \]
where \( k \) is some integer (the quotient).

### Step 2: Calculate \( 4n \)
Now, we need to find \( 4n \):
\[ 4n = 4(129k + 27) = 516k + 108 \]

### Step 3: Divide \( 4n \) by 86
Next, we need to find the remainder when \( 4n \) is divided by 86. We can express this as:
\[ 4n \mod 86 = (516k + 108) \mod 86 \]

### Step 4: Simplify \( 516k \mod 86 \)
First, we calculate \( 516 \mod 86 \):
\[ 516 \div 86 \approx 6 \quad (\text{since } 86 \times 6 = 516) \]
Thus, \( 516 \mod 86 = 0 \).

So, we have:
\[ (516k) \mod 86 = 0 \]

### Step 5: Simplify \( 108 \mod 86 \)
Next, we calculate \( 108 \mod 86 \):
\[ 108 - 86 = 22 \]
Thus, \( 108 \mod 86 = 22 \).

### Step 6: Combine the results
Now we combine the results:
\[ (516k + 108) \mod 86 = (0 + 22) \mod 86 = 22 \]

### Conclusion
Therefore, the remainder when \( 4n \) is divided by 86 is:
\[ \text{Remainder} = 22 \]