Arrangement (i):

Let the expense a bat be x and cost of a ball be y.

As per the inquiry,

\[7x\text{ }+\text{ }6y\text{ }=\text{ }3800\text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }.\text{ }\left( I \right)\]

\[3x\text{ }+\text{ }5y\text{ }=\text{ }1750\text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }.\text{ }\left( II \right)\]

From (I), we get

\[y\text{ }=\text{ }\left( 3800-7x \right)/6\ldots \text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }..\left( III \right)\]

Subbing (III) in (II). we get,

\[3x+5\left( 3800-7x \right)/6\text{ }=1750\]

$\Rightarrow 3x+\text{ }9500/3-35x/6\text{ }=1750$

\[\Rightarrow 3x-35x/6\text{ }=\text{ }1750-9500/3\]

\[\Rightarrow \left( 18x-35x \right)/6\text{ }=\text{ }(5250-9500)/3\]

\[\Rightarrow -17x/6\text{ }=\text{ }-\text{ }4250/3\]

\[\Rightarrow -17x\text{ }=\text{ }-\text{ }8500\]

\[x\text{ }=\text{ }500\text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }..\text{ }\left( IV \right)\]

Subbing the worth of x in (III), we get

\[y\text{ }=\text{ }\left( 3800-7\text{ }\times 500 \right)/6\text{ }=\text{ }300/6\text{ }=\text{ }50\]

Consequently, the expense of a bat is Rs 500 and cost of a ball is Rs 50.

Arrangement (ii):

Leave the decent charge alone Rs x and per km charge be Rs y.

\[x\text{ }+\text{ }10y\text{ }=\text{ }105\text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }..\text{ }\left( 1 \right)\]

\[x\text{ }+\text{ }15y\text{ }=\text{ }155\text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }..\text{ }\left( 2 \right)\]

From (1), we get

\[x\text{ }=\text{ }105\text{ -}10y\text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }.\text{ }\left( 3 \right)\]

Subbing the worth of x in (2), we get

$105\text{ – }10y\text{ }+\text{ }15y\text{ }=155$

\[5y\text{ }=\text{ }50\]

\[y\text{ }=\text{ }10\text{ }\ldots \text{ }\ldots \text{ }\ldots \text{ }..\text{ }\left( 4 \right)\]

Placing the worth of y in (3), we get

\[x\text{ }=\text{ }105\text{ -}10\text{ }\times \text{ }10\text{ }=\text{ }5\]

Thus, fixed charge is Rs 5 and per km charge = Rs 10

Charge for

\[25\text{ }km\text{ }=\text{ }x\text{ }+\text{ }25y\text{ }=\text{ }5\text{ }+\text{ }250\text{ }=\text{ }Rs\text{ }255\]