The cost price of 24 fans is equal to the selling price of 32 fans. fi

1.	The cost price of 24 fans is equal to the selling price of 32 fans. find gain or loss in per cent
Answer» $\large\underline{\bf{Solution-}}$ 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, $\rm :\longmapsto\:Loss\% = \dfrac{Loss}{Cost \: Price} \times 100\%$ $\rm :\longmapsto\:Loss\% = \dfrac{8}{32} \times 100\%$ $\bf\implies \:Loss = 25\%$ $\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{(100+Gain \% )\: (or)(100 - Loss\%)}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

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

Answer»

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

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,

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

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

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

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