Question

If the cost of 20 pens is equal to the selling price of 16 pens. What is the gain or loss % ?

Answer 1

Answer:

$\red{ \boxed{\texttt{Answer}}}$

Let 16 pens cost Rs.100. Hence 1 pen will cost 100/16.

SP of 12 pens = Rs.100. Hence SP of 1 pen = 100/12

Profit = 100/12 - 100/16= 800-600/96 or 200/96

Or 25/12.

Proit % = profit ÷ cp x 100 = 25/12 × 16/100 x100

= 100/3 or 33.33%

Answer 2

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

↝Let assume that Cost Price of 1 pen = Re 1

So,

↝Cost Price of 16 pens = Rs 20

↝Cost price of 20 pens = Rs 20

According to statement,

↝Selling Price of 16 pens = Cost Price of 20 pens.

It implies,

↝Selling Price of 16 pens = Rs 20

Now, we have

↝Cost Price of 16 pens = Rs 16

↝Selling Price of 16 pens = Rs 20

Since, Selling Price > Cost Price

So, there is Profit in this transaction.

We know,

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

$\rm \: = \: \:20 - 16 = 20−16$

$\rm \: = \: \:4 = 4$

$\bf\implies \:Profit = Rs \: 4$

Now,

We know,

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

$\rm \: = \: \:\dfrac{4}{16} \times 100\:$

$\rm \: = \: \:25\%$

Hence,

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

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