Question

Kindly solve Angela question

Answer 1

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

Given that,

• Selling Price of the purse including sale tax = $ 138.60

• Rate of Sale tax = 10 %

Let assume that the price of the bag without sale tax be x.

So,

$\rm \: x + 10\% \times x = 138.60$

$\rm \: x + \dfrac{10}{100} \times x = 138.60$

$\rm \: x + \dfrac{x}{10} = 138.60$

$\rm \: \dfrac{10x + x}{10} = 138.60$

$\rm \: \dfrac{11x}{10} = 138.60$

$\rm \: 11x = 1386$

$\rm\implies \:x = 126$

So, Selling Price of purse without sale tax = 126

Now, we have to find the Marked Price of the purse.

We have

• Selling Price of purse = $ 126

• Discount % = 30 %

We know,

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

So, on substituting the values, we get

$\rm \: Marked \: Price \: = \: \dfrac{100 \times 126}{100 - 30}$

$\rm \: Marked \: Price \: = \: \dfrac{12600}{70}$

$\rm\implies \:Marked \: Price \: = \: 180$

So, Original price of the purse is $ 180.

So, option (E) is correct.

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

Additional Information :-

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