Question

The number of times $99$ is subtracted from $1111$ so that the remainder is less than $99$ is:

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

Answer: (B)

$11$

According to the definition of Euclid's division lemma,

$a=b\times q+r$ where $0\le r<b.$ {$r$ is remainder}

Let $x$ be the number of times $99$ is subtracted.

then by applying the Euclid’s Division Lemma, we get

$\Rightarrow 1111=99x+R$

$\Rightarrow 1111-99x=R$

$\Rightarrow 1111-99x<99$

$\Rightarrow 1111-99<99x$

$\Rightarrow 1012<99x$

Substitute $x=10$

$1012<990$

Further $x=11$

$⟹1012<99\left(11\right)$

$⟹1012<1089$

Thus it satisfies for $x=11$

Hence the required value is $11$.