Question

In the last summer vacation, Akshay was given an assignment of writing down numbers from $100$ to $1000$. Despite all his brilliance and intelligence, Akshay always gets confused between the digits $6$ and $9$. As a result, he ends up interchanging them. How many numbers did he write correctly in his assignment ?

• A. $343$
• B. $353$
• C. $448$
• D. $452$

Answer 1

The correct option is C $448$

Let us start by considering numbers starting from $100$ to $200$.

The numbers where Akshay can go wrong are:

$106,109,116,119,126,129,136,139,146,149,156,159,160,161,162,163,164,165,166,167,168,169,176,179,186,189,190,191,192,193,194,195,196,197,198,199$.

Hence, there are $36$ numbers.

Similarly, between $200$ and $300\Rightarrow 36$ numbers

between $300$ and $400\Rightarrow 36$ numbers

between $400$ and $500\Rightarrow 36$ numbers

between $500$ and $600\Rightarrow 37$ numbers

between $600$ and $700\Rightarrow 99$ numbers

between $700$ and $800\Rightarrow 36$ numbers

between $800$ and $900\Rightarrow 37$ numbers

between $900$ and $1000\Rightarrow 99$ numbers

In all, Akshay went wrong with $\Rightarrow 452$ numbers.

So, Akshay wrote $900-452=448$ numbers, correctly.