Question

In a divisor problem, the remainder is $6$ and the divisor is $5$ times the quotient and is obtained by adding to thrice of remainder. Find the dividend.

Answer 1

Hint: For solving above question, use the formula, Dividend$ = $divisor$ \times $quotient$ + $remainder. We substitute the known values in the formula and we find the unknown value.

Complete step-by-step answer:
In this question, we have to find a dividend.
Given, Remainder $\left( R \right) = 6$
From the question
Divisor $\left( D \right) = 5$ [According to given statement in question]
Let the quotient $ = x$
$\therefore $ Divisor $\left( d \right) = 5x.........(1)$
Or, $d = 3R + 2.........(2)$
Equating 1 and 2
$\therefore $$5x = 3R + 2$
Substituting the given value of R
${
  5x = 3\left( 6 \right) + 2 \\
  x = \dfrac{{20}}{5} \\
  \therefore x = 4 \\
} $
$\therefore $By equation $\left( 1 \right)$Divisor$ = 5 \times 4 = 20$.
We know that,
Dividend$ = $divisor$ \times $quotient$ + $remainder
${
   = 4 \times 20 + 6 \\
   = 80 + 6 \\
   = 86 \\
} $

Hence, the dividend is $86$.

Note: Concept of different terms & their formulations involved in division like divisor, dividend, quotient & remainder should be known to solve the problem. Basically, divisor is a number by which another number is to be divided whereas dividend is that number that is to be divided. Quotient is the result obtained by dividing dividend by divisor & remainder is the number left over from dividend after getting the quotient in integers.