If an number is divided by 15, it leaves remainder of 9. If four times the number is divided by 5, then what will be the remainder ?

Options

A. zero
B. 1
C. 2
D. 3

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Define the number
Let the number be \( n \).

### Step 2: Set up the equation based on the given information
According to the problem, when \( n \) is divided by 15, it leaves a remainder of 9. This can be expressed mathematically as:
\[ n = 15k + 9 \]
where \( k \) is some integer (the quotient when \( n \) is divided by 15).

### Step 3: Calculate four times the number
Now, we need to find \( 4n \):
\[ 4n = 4(15k + 9) = 60k + 36 \]

### Step 4: Divide \( 4n \) by 5
Next, we will divide \( 4n \) by 5 and find the remainder:
\[ 4n = 60k + 36 \]
We can separate this into two parts:
\[ 60k \div 5 \quad \text{and} \quad 36 \div 5 \]

### Step 5: Calculate the remainder of \( 60k \div 5 \)
Since \( 60k \) is a multiple of 5, it will leave a remainder of 0:
\[ 60k \div 5 = 12k \quad \text{(no remainder)} \]

### Step 6: Calculate the remainder of \( 36 \div 5 \)
Now, we need to find the remainder when 36 is divided by 5:
\[ 36 \div 5 = 7 \quad \text{(quotient)} \]
\[ 5 \times 7 = 35 \]
The remainder is:
\[ 36 - 35 = 1 \]

### Step 7: Combine the results
Since \( 60k \) gives a remainder of 0 and \( 36 \) gives a remainder of 1, the total remainder when \( 4n \) is divided by 5 is:
\[ 0 + 1 = 1 \]

### Final Answer
Thus, the remainder when \( 4n \) is divided by 5 is **1**.

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