Question

A man buys two horses for Rs.$1550$.He sells one so as to lose $23$% and the other so as gain $27$%.On the whole he neither gain nor loses.what does each horse cost ?

• A. Rs.$807$,Rs.$743$
• B. Rs.$817$,Rs.$733$
• C. Rs.$827$,Rs$723$
• D. Rs.$837$,Rs.$713$

Answer 1

Answer: (D)

Rs.$837$,Rs.$713$

Let, the cost price of first horse is $xRs.$ and cost price of second horse is $yRs.$

Hence,

$x+y=1550Rs.\dots .\left(1\right)$

Now, He sells first horse at loss of $23\%$

Hence, $loss=\frac{23}{100}x$

He sells second horse at profit of $27\%$

Hence, $profit=\frac{27}{100}y$

Given that on the whole he neither profited nor loses.

Hence,

$profit=loss$

or

$\frac{23}{100}x-\frac{27}{100}y=0$

$23x-27y=0\dots .\left(2\right)$

Solving equation (1) and (2) we get

Put value of $y$ from (1) to (2)

$23x-27(1550-x)=0$

$23x+27x-27\times 1550=0$

$50x=27\times 1550$

$x=\frac{27\times 1550}{50}$

$x=27\times 31$

$x=837Rs.\dots \left(3\right)$

put value of $x$ from (3) to (1) we get

$837+y=1550$

$y=1550-837$

$y=713Rs....\left(4\right)$

Hence cost price of two horses is

$Rs.837,Rs.713$