CAT 2022 Slot 3 Paper

Let the number of 100 cheques, 250 cheques and 500 cheques be $\mathit{x},\mathit{y}$ and $\mathit{z}$ respectively.
We need to find the maximum value of $\mathit{z}$.
$\mathit{x}+\mathit{y}+\mathit{z}=100$ $...\left(1\right)$
$100\mathit{x}+250\mathit{y}+500\mathit{z}=15250$
$2\mathit{x}+5\mathit{y}+10\mathit{z}=305$ $...\left(2\right)$
$2\mathit{x}+2\mathit{y}+2\mathit{z}=200$ $...\left(1\right)$
$\mathrm{Eqs}\left(2\right)-\left(1\right)$, we get
$3\mathit{y}+8\mathit{z}=105$
At $\mathit{z}=12,\mathit{x}=3$
Therefore, maximum value $\mathrm{z}$ can take is 12 .