$10$ people went to a restaurant to have a meal as a group. Of these, $9$ had already contributed Rs $400$ each, while the $10^{\text{th}}$ person had to give the entire additional amount required to honour the restaurant's bill. How much did this person pay if he had to pay Rs $900$ more than the group's average?

Let the total bill be Rs $x$.

Amount paid by $9$ people:

$9\times 400=3600$

So, amount paid by the $10^{\text{th}}$ person is:

$x-3600$

Group average is:

$\frac{x}{10}$

According to the question,

$x-3600=\frac{x}{10}+900$

$x-\frac{x}{10}=4500$

$\frac{9x}{10}=4500$

$x=5000$

So, amount paid by the $10^{\text{th}}$ person is:

$x-3600=5000-3600$

$=1400$