Question

67. A shop keeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8% on the discounted price. If the customer pays Rs. 3,402 as the price including the sales tax, then the marked price ​

Answer 1

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

Let assume that selling price of article exclusive of sales tax be Rs x

Given that, a sales tax of 8% is levied on the discounted price and the customer pays Rs. 3,402 as the price including the sales tax.

So, we have

$\rm \: x + 8\% \: of \: x \: = \: 3402$

$\rm \: x + \frac{8}{100} \: \times \: x \: = \: 3402$

$\rm \: x + \frac{2x}{25} \: = \: 3402$

$\rm \: \frac{25x + 2x}{25} \: = \: 3402$

$\rm \: \frac{27x}{25} \: = \: 3402$

$\rm\implies \:x \: = \: Rs \: 3150$

Now,

Selling Price = Rs 3150

Discount % = 10 %

We know, Marked Price, Selling Price and Discount % are interrelated by the symbol

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

So, on substituting the values, we get

$\rm \: Marked \: Price = \dfrac{100 \times 3150}{100 - 10}$

$\rm \: Marked \: Price = \dfrac{100 \times 3150}{90}$

$\rm \: Marked \: Price = \dfrac{100 \times 315}{9}$

$\rm \: Marked \: Price = 35 \times 100$

$\rm\implies \boxed{ \rm{ \:\:Marked \: Price \: = \: Rs \: 3500 \: \: }}$

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

Additional Information :-

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

Answer 2

$\rm \bigstar \underline{ \underline{Information \: \: mentioned \: in \: above \: question :}}$

• A shop keeper allows a discount of 10% on the marked price of an item but charges a sales tax of 8% on the discounted price.

• The the customer pays Rs. 3,402 as the price including the sales tax

$\rm \bigstar \underline{ \underline{What \: we \: \: have \: to \: calculate :}}$

$\mapsto \small \text{The required marked price}$

$\rm \huge \: \bigstar \underline{ \underline{Solution :}}$

$\rm \bigstar \underline{ \underline{Assumption :}}$

$\mapsto \small \text {Consider the marked price be x Rs}$

$\rm{Then , \: 108 \: \% \: of \: 90 \: \% \: of \: x = 3,402 }$

$\rm \bigstar \underline{ \underline{So :}}$

$\rm \implies \dfrac{108}{100} \times \dfrac{90}{100} \: x = 3,402$

$\rm \implies \: x = \bigg( \dfrac{340,200 \times 100}{108 \times 90} \bigg)$

$\rm \implies \: x = \bigg( \dfrac{34,020,000}{9,720} \bigg)$

$\bf \implies \: x = 3,500 \: Rs$

$\rm \bigstar \underline{ \underline{Therefore:}}$

$\mapsto \small \text{The required marked price is}$

$\bf \longrightarrow \: \purple{x } \green{ = } \pink{ 3,500 }\: \red{ Rs }$