Question

A man buys $2$ Cow for $Rs.2700$ and sells one for loss of $6$ $\%$ and on other he gains $7.5$ $\%.$, On the whole, he neither gained nor lost. What does $2^{nd}$ Cow cost?

• A. Rs. $1100$
• B. Rs. $1200$
• C. Rs. $1000$
• D. Rs. $6075$

Answer 1

The correct option is B Rs. $1200$

Let the cost of $2^{nd}$ cow be Rs. $x$

and the cost of $1^{st}$ cow $=Rs2700-x$

Profit of $7.5$% on the second cow.

$SP=CP\left(\frac{100-P\%}{100}\right)$

$=x\left(\frac{100+7.5}{100}\right)=\frac{1075}{1000}x.$

Loss of $6$% on the first cow

$SP=(2700-x)\left(\frac{100-6}{100}\right)=\frac{94(2700-x)}{100}$

Since these is no profit or loss in the overall transaction, we have

$\frac{1075}{1000}\times \frac{940(2700-x)}{1000}=2700$

$1075x-940x+940\times 2700=2700\times 1000$

$135x+940\times 2700=2700\times 1000$

$135x=2700\times 60$

$x=\frac{2700\times 60}{135}=20\times 60$

$x=1200$

$\therefore$ The price of the $2^{nd}$ cow = Rs $1200.$