A shopkeeper sells a sweater at a loss of $5 %$ . If he had sold it for Rs. $260$ more, he would have made a profit of $15 %$ . Calculate the purchase price of the sweater.

1900

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1400

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1000

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1300

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Solution

The correct option is D Rs $1300$
case1:Let CP be $x$
Loss=5%
$S P_{1} = x - 5 % o f x$
$S P_{1} = 95 % o f x = \frac{95}{100} x$

Case2: CP $= x$ ,
$P_{2} = 15 %$
$S P_{2} = x + 15 % o f x = \frac{115}{100} x$

Difference in SP is given $260$
Thus,
$\begin{matrix} S P_{2} - S P_{1} = 260 \frac{115 x - 95 x}{100} = 260 \Rightarrow 20 x = 260 \times 100 \Rightarrow x = \frac{26000}{20} \Rightarrow x = 1300 \end{matrix}$
Thus purchase price is $1300$ Rs.

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A shopkeeper sells a sweater at a loss of 5%. If he had sold it for Rs. 260 more, he would have made a profit of 15%. Calculate the purchase price of the sweater.

The correct option is D Rs 1300case1:Let CP be x Loss=5%SP1=x−5%ofxSP1=95%ofx=95100xCase2: CP=x,P2=15%SP2=x+15%ofx=115100xDifference in SP is given 260Thus,SP2−SP1=260115x−95x100=260⇒20x=260×100⇒x=2600020⇒x=1300Thus purchase price is 1300 Rs.

A shopkeeper sells a sweater at a loss of $5 %$ . If he had sold it for Rs. $260$ more, he would have made a profit of $15 %$ . Calculate the purchase price of the sweater.