Question

Neil bought 30 kg rice at the rate of Rs. 9.50/kg and 40 kg of rice at the rate of Rs. 8.50/kg and mixed them. She sold the mixture at the rate of Rs. 8.90/kg. Find the total profit or loss in the whole transaction.

Answer 1

Hint: Difference between the selling price and cost price gives the value of either profit or loss.
If \[n{\rm{ units}}\] of goods are produced with the unit price of $ {\rm{Rs}}{\rm{. }}m $ , then the total cost of the goods is given by $ {\rm{Rs}}{\rm{. }}\left( {n \times m} \right) $ .

Complete step-by-step answer:
Let us assume $ {x_{30}} $ and $ {y_{40}} $ be the total cost price for 30 kg rice and 40 kg rice respectively.
The cost price of 30 kg rice can be determined by the product of unit price and the quantity of rice.
Therefore, the total cost price for 30 kg rice is given by
  $
\Rightarrow {x_{30}} = 30 \times 9.50\\
 = {\rm{Rs}}{\rm{. }}285{\rm{ }}
 $
The cost price of 40 kg rice can be determined by the product of unit price and the quantity of rice.
Therefore, the total cost price for 40 kg rice is given by
  $
\Rightarrow {x_{40}} = 40 \times 8.50\\
 = {\rm{ Rs}}{\rm{. 340}}
 $
The weight of the mixture is $ 30 + 40 = 70 $ kg.
The selling price for the mixture per kg is Rs. 8.90/kg.
The selling price for the mixture can be determined by the product of the quantity of the mixture and its unit price.
Let, $ {s_{70}} $ be the total selling price of the mixture.
Therefore, the total selling price of the mixture is given by
 $
\Rightarrow {s_{70}} = 70 \times 8.90\\
 = {\rm{Rs}}{\rm{. }}623
 $
 $ {s_{70}} = {\rm{Rs}}{\rm{. 623}}......\left( 1 \right) $
We know that the difference between the cost price and selling gives the value of either profit or loss.
When, selling price is greater than the cost price, the seller gains profit.
The total cost price $ = {x_{30}} + {y_{40}} $
  $
\Rightarrow {x_{30}} + {y_{40}} = 285 + 340\\
 = 625
 $
 $ {x_{30}} + {y_{40}} = 625......\left( 2 \right) $
Therefore, from equation (1) and (2), we can conclude that the cost price is more than selling price. Hence, Neil would face a loss.
Let $ l $ denotes the loss faced by Neil.
Loss can be calculated by subtracting selling price from the cost price.
Loss = Cost Price – Selling Price
Loss can be calculated as
  $
\Rightarrow l = {x_{30}} + {y_{40}} - {s_{70}}\\
 = 625 - 623\\
 = 2
 $
Therefore, Neil faced a loss of Rs. 2.

Note: In this type of question, special care should be taken while declaring whether the seller has gained profit or suffered a loss. Keep in mind the concept that the selling price if greater than cost price gives profit. But, when the cost price is greater than the selling price, the seller suffers a loss.