Question : An article was sold at a profit of 12%. If the cost price is 10% less and the selling price would be Rs. 5.75 more, there would be a profit of 30%. Then at what price it should be sold to make a profit of 20%?
Option 1: Rs. 115
Option 2: Rs. 120
Option 3: Rs. 138
Option 4: Rs. 215
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Correct Answer: Rs. 138
Solution :
Let the original cost price be Rs. 100$x$.
Given that the article was sold at a profit of 12%.
⇒ The original selling price = 100$x$ + 12% of 100$x$ = 112$x$
Now, if the cost price is 10% less, the new cost price = 90% of the original cost price = 90$x$
Given that there would be a profit of 30% with the new cost price and selling price.
⇒ New selling price = 130% of the new cost price = 117$x$
According to the question,
117$x$ – 112$x$ = 5.75
⇒ 5$x$ = 5.75
$\therefore$ $x$ = 1.15
So, the original cost price = 100 × 1.15 = Rs. 115
Now, to make a profit of 20%, the selling price = 120% of 115 = Rs. 138
Hence, the correct answer is Rs. 138.
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