Question

the cost price of 24 fans is equal to the selling price of 32 fans. find gain or loss in per cent​

Answer 1

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

Let

• Cost Price of 1 fan = Re 1

So,

• Cost Price of 24 fans = Rs 24

and

• Cost Price of 32 fans = Rs 32

According to statement,

Selling Price of 32 fans = Cost Price of 24 fans

It implies,

• Selling Price of 32 fans = Rs 24

Now, we have

• Cost Price of 32 fans = Rs 32

• Selling Price of 32 fans = Rs 24

• It implies, Selling Price < Cost Price

Hence, there is loss in this transaction.

We know,

$\rm :\longmapsto\:Loss = Cost \: Price \: - \: Selling \: Price$

$\rm :\longmapsto\:Loss = 32 - 24$

$\rm :\longmapsto\:Loss = Rs \: 8$

Now,

We know,

$\rm :\longmapsto\:Loss\% = \dfrac{Loss}{Cost \: Price} \times 100\%$

$\rm :\longmapsto\:Loss\% = \dfrac{8}{32} \times 100\%$

$\bf\implies \:Loss = 25\%$

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