Question

A man buys two horses for 1,350. He sells one so as to lose 6% and the other so as to gain 7.5%. On the whole he neither gains nor loses. What does each horse cost ?​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

• A man buys two horses for 1,350.

• He sells one so as to lose 6% and the other so as to gain 7.5%.

• On the whole he neither gains nor loses.

Let assume that

• Cost Price of first horse be Rs x

• Cost Price of second horse be Rs 1350 - x

Consider Case - 1

Cost Price of horse = Rs x

Loss % = 6 %

We know,

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: SP = \frac{(100 - Loss\%) \times CP}{100} \: }}}$

So, Selling Price of horse is

$\rm :\longmapsto\:SP_1 = \dfrac{(100 - 6) \times x}{100}$

$\rm :\longmapsto\:SP_1 = \dfrac{(94) \times x}{100}$

$\rm \implies\:\boxed{ \tt{ \: SP_1 = \frac{94x}{100} \: }} - - - - (1)$

Consider Case - 2

Cost Price of horse = Rs x

Gain % = 7.5 %

We know,

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: SP = \frac{(100 + Gain\%) \times CP}{100} \: }}}$

So, Selling Price of second horse is

$\rm :\longmapsto\:SP_2 = \dfrac{(100 + 7.5) \times (1350 - x)}{100}$

$\rm \implies\:\boxed{ \tt{ \: SP_2 = \frac{1075(1350 - x)}{1000} \: }}$

According to statement

$\rm :\longmapsto\:SP_1 + SP_2 = CP_1 + CP_2$

$\rm :\longmapsto\:SP_1 + SP_2 = x + 1350 - x$

$\rm :\longmapsto\:SP_1 + SP_2 = 1350$

$\rm :\longmapsto\:\dfrac{94x}{100} + \dfrac{1075(1350 - x)}{1000} = 1350$

$\rm :\longmapsto\: \dfrac{940x + 1075(1350 - x)}{1000} = 1350$

$\rm :\longmapsto\: \dfrac{940x + 1451250 - 1075x}{1000} = 1350$

$\rm :\longmapsto\: \dfrac{1451250 - 135x}{1000} = 1350$

$\rm :\longmapsto\:1451250 - 135x = 1350000$

$\rm :\longmapsto\: - 135x = 1350000 - 1451250$

$\rm :\longmapsto\: - 135x = - 101250$

$\bf\implies \:x = 750$

So,

Cost Price of first horse be Rs 750

Cost Price of second horse be Rs 1350 - 750 = Rs 600

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More to know

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain\%) \: or \: (100 - Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$