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Word Problem* 8_

Problem 8: A shopkeeper sales a pen for 13.20 Rs and gets a profit of 10%. If he wants to increase his profit to the limit of 15%, then at what price should he sale the pens ?

a) 13.53 Rs                   b) 13.72 Rs                            c) 13.80 Rs                    d) 13.86 Rs

 



Solution:

We suppose Cost Price (CP) of Pen is ‘x’

i-e CP = x

We  are given that  Sale Price (SP) is 13.20 Rs

i-e

SP= 13.20Rs

Also given that profit is 10 % of CP i-e;

Profit = P = \frac{10}{100}\times x

We know the profit formula

P = SP - CP

Put respective values

\Rightarrow \frac{10}{100}\times x = 13.20 - x

Shifting ‘x’ terms to one side

\Rightarrow \frac{1}{10}x+x=13.20

Simplifying,

\Rightarrow \frac{11}{10}x=13.20

\Rightarrow x = \frac{10}{11}\times 13.20

\Rightarrow x =12

So, we have calculated CP as Rs 12

Now Come to Condition

If  we want to earn 15% profit of cost price i-eProfit = P = \frac{15}{100}x

Then what should be the SP ?

SP = ?

We Know  P = SP - CP

Put values of condition !

\frac{15}{100}x = SP - x

Shift ‘x’ terms to one side

\Rightarrow \frac{15}{100}x + x= SP

\Rightarrow \frac{115}{100}x = SP

or

\Rightarrow SP = \frac{115}{100}x

Put value of x

\Rightarrow SP = \frac{115}{100}\times 12

\Rightarrow SP = 13.80 Rs

So he should sale it for 13.80 Rs for earning 15% profit

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