Question

If an article is sold for Rs. 105 there is loss of 9% .At what price should be article be sold so that there is a gain of 30%?

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Answer 1

Explanation:

Step 1:

The selling price of an article = Rs. 105

Loss = 9%

Therefore,

The C.P. of the article

= \frac{100}{100-L}

100−L

100

* S.P.

= \frac{100}{100-9}

100−9

100

* S.P.

= \frac{100}{91}

91

100

* 105

= Rs. 115.38

Step 2:

Gain = 30%

Thus,

The S.P. of the article should be, in order to have a gain of 30%,

= \frac{100+P}{100}

100

100+P

* C.P.

= \frac{100+30}{100}

100

100+30

* 115.38

= \frac{130}{100}

100

130

* 115.38

= 149.99

≈ Rs. 150

Answer 2

Clarification :

Here, we are given that the selling price of the article at the loss of 9% is 105. So, through these given information, we will calculate the cost price of the article.Then by the formula of selling price when desired gain and cost price is given we will calculate the selling price at the gain of 30%.

Given :

• Selling selling price of the article at a loss of 9% = Rs 105.

To calculate :

• At what price should be article be sold so that there is a gain of 30% ?

Calculation :

As, we are provided :

$\longmapsto \: \pmb{ \rm{ \pink{Selling \: Price =Rs. \: 105 }}} \\ \longmapsto \: \pmb{ \rm{ \pink{Loss \: \% =9 \: \% }}}$

So, let's calculate the cost price of the article.

As we know that,

$\underline{ \boxed{ \pmb{ \rm{Cost \: Price =Rs. \: \Bigg \lgroup \dfrac{100}{100- Loss \: \% } \times SP\Bigg \rgroup }}}} \\ \\ \\ \longrightarrow \sf{Cost \: Price =Rs. \: \Bigg \lgroup \dfrac{100}{100- 9} \times105 \Bigg \rgroup} \\ \\ \\ \longrightarrow \sf{Cost \: Price =Rs. \: \Bigg \lgroup \dfrac{100}{91} \times105 \Bigg \rgroup} \\ \\ \\ \longrightarrow \boxed{\rm{ \pink{Cost \: Price =Rs. \: \Bigg \lgroup \dfrac{10500}{91} \Bigg \rgroup} }}$

Henceforth, cost price of the article is Rs. $\sf {\dfrac{10500}{91} }$.

Now, we have :

$\longmapsto \: \pmb{ \rm{ \pink{ Cost\: Price =Rs. \: \dfrac{10500}{91} }}} \\ \\ \longmapsto \: \pmb{ \rm{ \pink{ Desired \: Gain\: \% =30\: \% }}}$

So,

$\underline{ \boxed{ \pmb{ \rm{Desired \:SP =Rs. \: \Bigg \lgroup \dfrac{100 +Gain\: \% }{100 } \times CP\Bigg \rgroup }}}} \\ \\ \\ \longrightarrow \: \sf{Desired \:SP =Rs. \: \Bigg \lgroup \dfrac{100 +30}{100 } \times \dfrac{10500}{91} \Bigg \rgroup} \\ \\ \\ \longrightarrow \: \sf{Desired \:SP =Rs. \: \Bigg \lgroup \dfrac{13 \cancel{0}}{10 \cancel0 } \times \dfrac{10500}{91} \Bigg \rgroup} \\ \\ \\ \longrightarrow \: \sf{Desired \:SP =Rs. \: \Bigg \lgroup \dfrac{13}{ \cancel{10} } \times \dfrac{ \cancel{10500}}{91} \Bigg \rgroup} \\ \\ \\ \longrightarrow \: \sf{Desired \:SP =Rs. \: \Bigg \lgroup \cancel{13 }\times \dfrac{1050}{ \cancel{91}} \Bigg \rgroup} \\ \\ \\ \longrightarrow \: \sf{Desired \:SP =Rs. \: \Bigg \lgroup \dfrac{1050}{7} \Bigg \rgroup} \\ \\ \\ \longrightarrow \: \boxed{ \rm \pink{Desired \:SP =Rs. \: 150} }$

Therefore, at Rs. 150 should be article be sold so that there is a gain of 30%.