Solve the following:

A man was engaged as typist for the month of february in $2009.$ He was paid $Rs.500$ per day, but $Rs.100$ per day were deducted for the days he remained absent. He received $Rs.9100$ as salary for the month. For how many days did he work?

Let the man worked as a typist for $x$ days in the month of February $2009.$

Then, absent in the month of February $2009=(28-x)$ days [we know that, number of days in month of February 2009 is 28]

Per day payment $=Rs.500$

Total paid amount for working days $=Rs.500x$

And per day deduction, when he remained absent $=Rs.100$

Total amount deducted for being absent $=Rs.100\times (28-x)$

Given, salary received by man for the month of February is $Rs.9100.$

According to the question, we have

$500x-100(28-x)=9100$

$\Rightarrow 500x-2800+100x=9100$

$\Rightarrow 600x=9100+2800$

$\Rightarrow 600x=11900$

$\Rightarrow x=\frac{11900}{600}$

$\therefore x=19.83=20$(approx)

Therefore, the man worked for $20$ days.