In a question on division, the divisor is 7 times the quotient and 3 times the remainder. If the remainder is 28, then the dividend is

Options

A. 588
B. 784
C. 823
D. 1036

Answer

To solve the problem step by step, let's denote the variables as follows:

- Let the quotient be \( Q \).
- Let the divisor be \( D \).
- Let the remainder be \( R \).

According to the problem, we have the following relationships:

1. The divisor \( D \) is 7 times the quotient \( Q \):
\[ D = 7Q \]

2. The divisor \( D \) is also 3 times the remainder \( R \):
\[ D = 3R \]

3. The remainder \( R \) is given as 28:
\[ R = 28 \]

Now, we can substitute the value of \( R \) into the second equation to find \( D \):

### Step 1: Calculate the Divisor \( D \)
Substituting \( R = 28 \) into \( D = 3R \):
\[ D = 3 \times 28 = 84 \]

### Step 2: Calculate the Quotient \( Q \)
Now that we have \( D \), we can substitute \( D = 84 \) into the first equation \( D = 7Q \):
\[ 84 = 7Q \]
To find \( Q \), divide both sides by 7:
\[ Q = \frac{84}{7} = 12 \]

### Step 3: Calculate the Dividend \( N \)
The formula for the dividend \( N \) in terms of the divisor, quotient, and remainder is:
\[ N = D \times Q + R \]
Substituting the values we found:
\[ N = 84 \times 12 + 28 \]

### Step 4: Perform the Multiplication and Addition
First, calculate \( 84 \times 12 \):
\[ 84 \times 12 = 1008 \]
Now add the remainder:
\[ N = 1008 + 28 = 1036 \]

### Final Answer
Thus, the dividend is \( N = 1036 \).

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