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Word Problem 15 (finding cost price for a sale price)

Problem 15: A person bought an article and sold it at a gain of 5%, Had he bought it at 5% less and sold it for Rs 1 less, he would have made a profit of 10%, Find the cost price of the article.

a. Rs 100                         b. Rs 150                           c. Rs 200                           d. Rs 500

Solution:

We suppose cost price = cp= Rs y

Given he earns profit of 5%

\Rightarrow Profit = p= \frac{5y}{100}

\Rightarrow p= \frac{y}{20}

So, from there we can find sale price sp by formula

p=sp-cp

\Rightarrow sp=p+cp

put values;

\Rightarrow sp=y+ \frac{y}{20}= \frac{21y}{20}

—————now come to the situation described ————-

Now if cp were to be 5% less then it would have been ;

cp= y- \frac{5y}{100}=\frac{19y}{20}

and sp with Re 1 less would have been;

sp=\frac{21y}{20}-1

Then by given condition profit would have been earned 10% more of 5% less cost price, i-e

p=\frac{10}{100}(\frac{19y}{20})

But we know

p=sp-cp

Put situational  values of  p, sp and cp

\Rightarrow \frac{10}{100}(\frac{19y}{20})=\frac{21y}{20}-1 - \frac{19y}{20}

\Rightarrow \frac{1}{10}(\frac{19y}{20})=\frac{y}{10}-1

\Rightarrow \frac{19y}{20}=y-10

\Rightarrow 19y=20y-200

\Rightarrow y=200

So, the option c is correct answer

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