Question

A trader allows 20% discount on the marked price of an article and still gains 11 1/9% If the cost pre
increases by 20%. how much discount percent should he now give on the same marked price to get the same
profit percentage as before?​

Answer 1

Answer:

Rs.100

Step-by-step explanation:

Marked price = Rs. 150

Percentage of discount = 20%

S=80%of150=(80100)×150=Rs.120

S= Rs. 120 and gain % = 20%

S = 120% of C.

120=120100×C⇒C=120×100120⇒C=Rs.100

∴ cost price=Rs.100

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Answer 2

The required discount percentage is 4.17%.

Step-by-step explanation:

Given:

20 percentage discount on the marked price of an article is allowed by a trader.

Gain of trader is  11 1/9%.

If cost price is increased  by 20 percentage.

To keep the same profit (%) percentage as before.

To Find:

The required discount  (%)percentage.

Formula used:

Selling Price= Cost Price x(100+Profit%)/100     ------------- formula no.01.

Selling Price   = Marked Price –  Discount              ----------- formula no.02

Selling Price  = {(100 + Profit %)/100} x Cost Price  ------------  formula no.03

Discount Percentage =[ (Marked Price – Selling Price )/Marked price] x 100     ------------ formula no.04

Solution:

Let the cost Price of the article is  Rupees 100.

As given-gain of trader is  11 1/9%.  

Gain $=11\frac{1}{9} \% =\frac{100}{9} \%= 11.11\%$

Applying formula no.01.

Selling Price of the article $=100 [ 1+\frac{11.11}{100} ]$

                                            $=111.11$

As given -20 percentage discount on the marked price of an article is allowed by a trader.

Applying formula no.02.

Selling Price  = Marked Price – Discount

           $111.11=Marked\ Price- Marked \ Price \ \times\frac{20}{100}$

           $111.11=Marked \ Price [1- \frac{20}{100} ]$

           $111.11=Marked\ Price [\frac{80}{100} ]$

           $Marked\ Price =\frac{111.11 \times100}{80}$

          $Marked\ Price = 138.89$                    

Marked Price on the article = 138.89

As given-  If cost price is increased  by 20 percentage.

Applying formula no.01.                                  

New the Cost Price of the article $=100[1+\frac{20}{100} ]$

                                                        $=120$

As given -to keep the same profit (% )percentage as before.

If profit  percentage is  remaining same then from formula no.03.

$Selling \ Price \propto \frac{1}{Cost\ Price }$

New Selling   Price of the article  $=\frac{120 \times 111.11}{100}$  

                                                       $= 133.33$

Applying formula no.04.

The discount percentage   $=\frac{( 138.89-133.33)}{133.33} \times 100$

                                              $= 4.17\%$

Thus, the required discount percentage is 4.17%.

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