Question

By selling 90 balls pens for 180 rupees a person loses 20% How many ball pens should he sell for rupees 96 so as to have a gain of 20% ​

Answer 1

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

Given that, By selling 90 balls pens for 180 rupees a person loses 20%.

It means,

Selling Price of 90 ball pens = Rs 180

So,

Selling Price of 1 ball pen = Rs 2

Loss % = 20 %

We know,

$\boxed{ \rm{ \:Cost \: Price \: = \: \frac{100 \times Selling \:Price}{100 - Loss\%} \: }}$

So, on substituting the values, we get

$\rm \: Cost \: Price \: = \: \dfrac{2 \times 100}{100 - 20}$

$\rm \: Cost \: Price \: = \: \dfrac{200}{80}$

$\rm\implies \:Cost \: Price \: = \: Rs \: 2.50$

Now,

Cost Price of 1 ball pen = Rs 2.50

Profit % = 20 %

We know,

$\boxed{ \rm{ \:Selling \: Price = \frac{(100 + Profit\%) \times Cost \: Price}{100} \: }}$

So, on substituting the values, we get

$\rm \: Selling \: Price = \dfrac{(100 + 20) \times 2.5}{100}$

$\rm \: Selling \: Price = \dfrac{120 \times 2.5}{100}$

$\rm\implies \:Selling \: Price \: = \: Rs \: 3$

So, it means Selling Price of 1 ball pen is Rs 3 to ensure profit of 20%

So, For Rs 96, the number of ball pens sold = 96 ÷ 3 = 32

Hence, 32 ball pens be sold for Rs 96 to get a profit of 20 %.

$\rule{190pt}{2pt}$

Additional Information :-

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