Question

A tradesman allows a discount of 15% on the written price. How much above the cost price he mark his goods to gain 70%?​

Answer 1

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

Let assume that Cost Price of good is Rs 100

Gain % = 70 %

We know, Selling Price, Cost Price and Gain % are connected by the relationship

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

So, on substituting the values, we get

$\rm \: Selling \:Price \: = \: \dfrac{(100 + 70) \times 100}{100}$

$\rm\implies \:Selling \: Price \: = \: Rs \: 170$

Now, we have

• Selling Price of good = Rs 170

• Discount % = 15 %

We know, Marked Price, Selling Price and Discount % are connected by the relationship

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

So, on substituting the values, we get

$\rm \: Marked \: Price \: = \: \dfrac{100 \times 170}{100 - 15}$

$\rm \: Marked \: Price \: = \: \dfrac{100 \times 170}{85}$

$\rm \: Marked \: Price \: = \: 100 \times 2$

$\rm\implies \:Marked \: Price \: = \: Rs \: 200$

So, we have now

• Cost Price of good = Rs 100

• Marked Price of good = Rs 200

So, it means Marked Price is double of the Cost Price.

So, 100 % above the cost price he mark his goods to gain 70% after allows a discount of 15 % on written price of good.

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

Additional Information :-

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