Question

The coach of a cricket team buys $7$ bats and $6$ balls for Rs. $3,800$. Later he buys $3$ bats and $5$ balls for Rs. $1,750$. The cost of each bat and each ball is

• A. Rs. $3,800;$ Rs. $1,750$
• B. Rs. $50;$ Rs. $500$
• C. Rs. $500;$ Rs. $50$
• D. Rs. $2150;$ Rs. $750$

Answer 1

The correct option is C Rs. $500;$ Rs. $50$

Suppose the cost of $1$ bat $=$ Rs. $x$ and cost of $1$ ball $=$ Rs. $y$ then
$7x+6y=\mathrm{3800......}eq\left(1\right)$
$3x+5y=\mathrm{1750......}eq\left(2\right)$
Multiply $3$ in $eq\left(2\right)$ and $7$ in $\left(1\right)$
$21x+18y=11400$
$21x+35y=12250$
Now on subtracting

$17y=850$
$\Rightarrow y=50$

Substituting this value of $y$ in eq. $\left(2\right)$,

$3x+5\left(50\right)=1750$

$\Rightarrow 3x=1500$

$\Rightarrow x=500$
Therefore,
Cost of $1$ bat $=500$ Rs.
Cost of $1$ ball$=50$ Rs.
Hence, option $C$ is correct.