A divisor is 15 times the quotient and 3 times the ramainder.If the remainder is 40,find the dividend.

Options

A. 1000
B. 600
C. 750
D. 900

Answer

To solve the problem step by step, we will use the information given in the question.

### Step 1: Identify the given values
- The remainder (R) is given as 40.
- The divisor (D) is 3 times the remainder.
- The divisor is also 15 times the quotient (Q).

### Step 2: Calculate the divisor
Since the remainder is 40, we can find the divisor:
\[ D = 3 \times R \]
\[ D = 3 \times 40 = 120 \]

### Step 3: Relate the divisor to the quotient
From the problem, we know that:
\[ D = 15 \times Q \]
Now substituting the value of D:
\[ 120 = 15 \times Q \]

### Step 4: Solve for the quotient
To find the quotient (Q), we rearrange the equation:
\[ Q = \frac{120}{15} \]
\[ Q = 8 \]

### Step 5: Use the formula for the dividend
The formula for the dividend (Div) is:
\[ \text{Dividend} = D \times Q + R \]
Substituting the known values:
\[ \text{Dividend} = 120 \times 8 + 40 \]

### Step 6: Calculate the dividend
Now we calculate:
\[ \text{Dividend} = 960 + 40 = 1000 \]

### Final Answer
The dividend is **1000**.

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