Question

In a question on division if four times the divisor is added to the dividend then how will the new remainder change in comparison with the original remainder.

Answer 1

Find the change in remainder

$\mathrm{Dividend}=\mathrm{Divisor}\times \mathrm{Quotient}+\mathrm{Remainder}$

Adding four times the divisor on both side

$\Rightarrow \mathrm{Dividend}+\left(4\times \mathrm{Divisor}\right)=\mathrm{Divisor}\times \mathrm{Quotient}+\left(4\times \mathrm{Divisor}\right)+\mathrm{Remainder}$

$\Rightarrow \mathrm{Dividend}+\left(4\times \mathrm{Divisor}\right)=\mathrm{Divisor}\times \left(\mathrm{Quotient}+4\right)+\mathrm{Remainder}$

Hence, there is no change in the remainder.