Question

21. How much percent more than the cost price should a
shopkeeper mark his goods, so that after allowing a
discount of 12.5% he should have a gain of 5% on
his outlay?​

Answer 1

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

Let assume that,

Marked Price of goods be Rs x

Discount % = 12.5 %

We know,

$\rm \: Selling\:Price = \dfrac{(100 - Discount\%) \times Marked\:Price}{100}$

So, on substituting the values, we get

$\rm \: Selling\:Price = \dfrac{(100 - 12.5) \times x}{100}$

$\rm \: Selling\:Price = \dfrac{87.5 \times x}{100}$

$\rm \: Selling\:Price = \dfrac{875 x}{1000} - - - (1)$

Now, we have

$\rm \: Selling\:Price = \dfrac{875 x}{1000}$

$\rm \: gain\% \: = \: 5\%$

We know,

$\rm \: Selling\:Price = \dfrac{(100 + gain\%) \times Cost\:Price}{100}$

So, on substituting the values, we get

$\rm \: \dfrac{875x}{1000} = \dfrac{(100 + 5) \times Cost\:Price}{100}$

$\rm \: \dfrac{175x}{2} = 105 \times Cost\:Price$

$\rm \: \dfrac{35x}{2} = 21 \times Cost\:Price$

$\rm \: \dfrac{5x}{2} = 3\times Cost\:Price$

$\rm\implies \:Cost\:Price = \dfrac{5}{6}x$

Now,

We have

$\rm \: \:Cost\:Price = \dfrac{5}{6}x$

$\rm \: Marked\:Price = x$

So, percentage of Market Price above the Cost price is

$\rm \: = \: \dfrac{Marked\:Price - Cost\:Price}{Cost\:Price} \times 100\%$

$\rm \: = \: \dfrac{x - \dfrac{5x}{6} }{\dfrac{5x}{6} } \times 100\%$

$\rm \: = \: \dfrac{ \dfrac{6x - 5x}{6} }{\dfrac{5x}{6} } \times 100\%$

$\rm \: = \: \dfrac{ \dfrac{x}{6} }{\dfrac{5x}{6} } \times 100\%$

$\rm \: = \: \dfrac{1}{5} \times 100\%$

$\rm \: = \: 20\%$

Hence,

20 % more than the cost price should a shopkeeper marked his goods, so that after allowing a discount of 12.5% he have a gain of 5% on his outlay.

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

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