On dividing 4996 by a certain number, the quotient is 62, and the remainder is 36. What is the divisor?

Options

A. 80
B. 85
C. 90
D. 95

Answer

To find the divisor when dividing 4996 by a certain number with a quotient of 62 and a remainder of 36, we can use the formula for division:

**Step 1: Understand the relationship between the numbers.**
The relationship can be expressed as:
\[ \text{Dividend} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder} \]

**Step 2: Substitute the known values into the formula.**
Here, the dividend is 4996, the quotient is 62, and the remainder is 36. So we can write:
\[ 4996 = (d \times 62) + 36 \]

**Step 3: Rearrange the equation to isolate the term with the divisor.**
Subtract the remainder from both sides:
\[ 4996 - 36 = d \times 62 \]
\[ 4960 = d \times 62 \]

**Step 4: Solve for the divisor (d).**
To find the divisor, divide both sides by 62:
\[ d = \frac{4960}{62} \]

**Step 5: Perform the division.**
Now, we will simplify \( \frac{4960}{62} \):
1. First, we can simplify by dividing both the numerator and denominator by 2:
\[ \frac{4960 \div 2}{62 \div 2} = \frac{2480}{31} \]

2. Now, we perform the division \( 2480 \div 31 \):
- 31 goes into 2480 approximately 80 times (since \( 31 \times 80 = 2480 \)).

Thus, we find:
\[ d = 80 \]

**Final Answer: The divisor is 80.**

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