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Q.

With the decrease in prices of coffee powder by 15%, the coffee shop was able to buy 2 kg more coffee powder with the same Rs.45 that he spent each month on buying coffee powder for his coffee shop, then the original price of coffee was Rs.[[1]].


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Detailed Solution

With the decrease in prices of coffee powder by 15%, the coffee shop was able to buy 2 kg more coffee powder with the same Rs.45 that he spent each month on buying coffee powder for his coffee shop, then the original price of coffee was Rs.3.97 per kg and the reduced price of coffee was Rs.3.38 per kg.
Let the original price of coffee powder per kg be Rs x.  
Let the coffee shop purchases y kg   coffee powder.
Therefore, the price for y kg   coffee powder = Rs xy.   It is given that the amount spent by the coffee shop to buy the coffee powder each month is Rs.45.
Therefore, we have got,
    xy=45   ⇒y= 45 x           ....(1)     Also, it is given that if there is a 15% decrease in the price of coffee powder, then the coffee shop will be able to buy 2 kg more coffee powder and the amount will remain the same.
Therefore, the coffee shop will purchase y+2 kg   coffee powder.
We know that,
Discount price = Marked price - Selling price
Discount %= Discount Price Market Price ×100%.  
⇒15 %= Discount Price x ×100%.   ⇒Discount price=Rs.  15 100 ×x  
Since, Discount price = Marked price - Selling price
⇒ 15 100 x=x− Selling price    ⇒Selling price=x− 15 100 x   ⇒Selling price= 85 100 x   And, it is given that after the discount, the price will be Rs.45, therefore, we get that 85 100 x y+2 =45   ⇒ 85 100 x 45 x +2 =45    ⇒ 85x 100 45+2x x =45   ⇒85 45+2x 100 =45    ⇒45+2x= 45×100 85    ⇒45+2x= 45×20 17   ⇒2x= 45×20 17 −45   ⇒2x=45 20 17 −1    ⇒x= 45 2 × 3 17    ⇒x=3.97   Therefore, the original price of coffee powder was Rs.3.97 per kg.
 
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