In a division sum, the divisor is 5 times the quotient and twice the remainder. If the remainder is 5, what is the number ?

Question

Accepted Answer

To solve the problem, we need to understand the relationship between the divisor, quotient, and remainder in the division operation. The problem states that the divisor is 5 times the quotient and twice the remainder. Given that the remainder is 5, we can use this information to find the number.

Let's break down the problem step by step:

1. **Given Information:**
   - Remainder = 5
   - Divisor = 2 × Remainder = 2 × 5 = 10
   - Divisor = 5 × Quotient

2. **Finding the Quotient:**
   - Since the divisor is 10 and it is also 5 times the quotient, we can set up the equation:
     $$
     10 = 5 \times \text{Quotient}
     $$
   - Solving for the quotient, we get:
     $$
     \text{Quotient} = \frac{10}{5} = 2
     $$

3. **Finding the Number:**
   - In a division operation, the number (dividend) can be expressed as:
     $$
     \text{Number} = (\text{Divisor} \times \text{Quotient}) + \text{Remainder}
     $$
   - Substituting the known values:
     $$
     \text{Number} = (10 \times 2) + 5 = 20 + 5 = 25
     $$

Thus, the number is 25, which corresponds to Option 3.

**Explanation for Incorrect Options:**

- **Option 1 (52):** 
  - If the number were 52, using the formula $(\text{Divisor} \times \text{Quotient}) + \text{Remainder} = 52$, and knowing the divisor is 10 and remainder is 5, the equation would not hold as it would require a different quotient that does not satisfy the given conditions.

- **Option 2 (15):**
  - If the number were 15, using the same formula, the equation $(10 \times \text{Quotient}) + 5 = 15$ would imply a quotient of 1, which contradicts the divisor being 5 times the quotient.

- **Option 4 (48):**
  - If the number were 48, the equation $(10 \times \text{Quotient}) + 5 = 48$ would imply a quotient of 4.3, which is not an integer and thus not valid in this context.

Therefore, Option 3 (25) is the only correct answer that satisfies all the given conditions of the problem.