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A man bought two cows in Rs. 410 and sold each of them at the same price and thereby gained $15 \%$ on one and lost $10 \%$ on the other. What was the C.P. of each cow ?

Solution-

Let the C.P. of first cow $=\mathrm{Rs} . x$

$\therefore \quad$ The C.P. of second cow

$=\mathrm{Rs} \cdot(410-x)$

From the question,

S.P. of first cow $=$ S.P. of second cow

$\Rightarrow \frac{x \times(100+15)}{100}$

$=\frac{(410-x)(100-10)}{100}$

$\Rightarrow 115 x=(410-x) \times 90$

$\begin{array}{l} \Rightarrow \quad 115 x=36900-90 x \\ \Rightarrow \quad 115 x+90 x=36900 \\ \Rightarrow \quad 205 x=36900 \end{array}$

$\therefore x=\frac{36900}{205}=180$

$\therefore \quad$ C.P. of 2 nd cow $=410-180$

$\text { =Rs. } 230$

$\therefore$ Rs. 180 , and Rs. $230 ;$ Ans.

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