Question

A shopkeeper bought 30 kg of rice at the rate of Rupees 90 per kg. He sold forty percent of the total quantity at the rate of Rupees 60 per kg. Approximately at what price per kg should he sell the remaining quantity to make 25\% overall profit?

• A. 155.5
• B. 167.5
• C. 157.5
• D. 147.5

Hint:

For mixed selling-price problems, first compute the \emph{target total revenue} using the desired overall profit on total cost. Subtract any revenue already realized, then divide by the remaining quantity to get the required price.

Answer 1

The Correct Option is D

Step 1: Compute total cost and target revenue
Cost price (CP) per kg \(= Rupees \; 90\). Total quantity \(=30\) kg.
Total CP \(= 30 \times 90 = Rupees \; 2700\).
Target profit \(=25\%\) \(\Rightarrow\) Required total selling price (SP)
\[ \Rightarrow \ \text{Target SP} = 2700 \times 1.25 = Rupees \;3375. \] Step 2: Revenue from the first part sold
40\% of 30 kg \(= 12\) kg sold at Rupees 60/kg.
Revenue from this part \(= 12 \times 60 = Rupees \; 720\). Step 3: Find needed price for the remaining quantity
Remaining quantity \(= 30 - 12 = 18\) kg.
Revenue still needed \(= 3375 - 720 = Rupees \; 2655\).
Required price per kg for the remaining \(= \dfrac{2655}{18} = Rupees \;147.5\). \[ \boxed{ \text{Sell the remaining at } Rupees \;147.5 \text{ per kg} } \]