Understanding the Division Sum Problem

This problem involves a standard division scenario where we need to find the dividend. We are given relationships between the divisor, quotient, and remainder, along with the value of the remainder. The fundamental relationship in any division sum is:

Dividend = (Divisor × Quotient) + Remainder

Let's denote:

• Dividend as $N$
• Divisor as $D$
• Quotient as $Q$
• Remainder as $R$

So the formula becomes: $N = (D \times Q) + R$.

Calculating the Divisor

The problem states:

• The divisor is 5 times the remainder.
• The remainder is given as 12.

We can write this mathematically as:

$D = 5 \times R$

Since $R = 12$, we can substitute this value:

$D = 5 \times 12$

$D = 60$

So, the divisor is 60.

Calculating the Quotient

The problem also states:

• The divisor is 10 times the quotient.

We can write this as:

$D = 10 \times Q$

We already found that the divisor ($D$) is 60. Substituting this value:

$60 = 10 \times Q$

To find the quotient ($Q$), we rearrange the equation:

$Q = \frac{60}{10}$

$Q = 6$

Therefore, the quotient is 6.

Calculating the Dividend

Now we have all the necessary components to find the dividend ($N$):

• Divisor ($D$) = 60
• Quotient ($Q$) = 6
• Remainder ($R$) = 12

Using the division formula $N = (D \times Q) + R$:

$N = (60 \times 6) + 12$

$N = 360 + 12$

$N = 372$

The dividend is 372.

Summary of the Division Sum

Here's a summary of the values we found:

The calculation confirms that the dividend is 372.