NIMCET Arithmetic Reasoning Previous Year Questions (PYQs) – Page 3 of 3

Given initial values:

$X=2,\quad Y=4$

Rule:

$X=\frac{XY}{2}$ and $Y=Y+1$

Now update step by step:

First iteration:

$X=\frac{2\times 4}{2}=4,\quad Y=5$

Second iteration:

$X=\frac{4\times 5}{2}=10,\quad Y=6$

Third iteration:

$X=\frac{10\times 6}{2}=30,\quad Y=7$

Fourth iteration:

$X=\frac{30\times 7}{2}=105,\quad Y=8$

Fifth iteration:

$X=\frac{105\times 8}{2}=420,\quad Y=9$

Sixth iteration:

$X=\frac{420\times 9}{2}=1890,\quad Y=10$

Seventh iteration:

$X=\frac{1890\times 10}{2}=9450$

Now $X=9450$, which is greater than $3000$.

So, the game stops.

Therefore, the final value of $X$ is $9450$.

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:

$x-3600=5000-3600$

$=1400$