In a division problem, the divisor is 4 times the quotient and 3 times the remainder. If remainder is 4, the dividend is

Options

A. 36
B. 40
C. 12
D. 30

Answer

To solve the problem, let's break it down step by step.

### Step 1: Understand the relationships
We know from the problem statement:
- The divisor (D) is 4 times the quotient (Q).
- The divisor (D) is also 3 times the remainder (R).
- The remainder (R) is given as 4.

### Step 2: Calculate the divisor
Since the remainder (R) is 4, we can find the divisor (D) using the relationship:
\[ D = 3 \times R \]
Substituting the value of R:
\[ D = 3 \times 4 = 12 \]

### Step 3: Calculate the quotient
Now, using the relationship that the divisor (D) is 4 times the quotient (Q):
\[ D = 4 \times Q \]
Substituting the value of D:
\[ 12 = 4 \times Q \]
To find Q, divide both sides by 4:
\[ Q = \frac{12}{4} = 3 \]

### Step 4: Calculate the dividend
The formula for the dividend (Div) in a division problem is given by:
\[ \text{Dividend} = (D \times Q) + R \]
Substituting the values of D, Q, and R:
\[ \text{Dividend} = (12 \times 3) + 4 \]
Calculating this:
\[ \text{Dividend} = 36 + 4 = 40 \]

### Final Answer
The dividend is **40**.

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