Final answer:
To calculate the cost price per kg for oranges sold by Mrs. Limbu after accounting for a 10% gain, the initial selling amount for the edible oranges (165 kg) was found first. After applying the gain percentage to the total selling price, the cost price was determined to be Rs 70 per kg, corresponding to Option A.
Step-by-step explanation:
The question asks to calculate the cost price of oranges per kilogram if Mrs. Limbu sold the remaining oranges after taking out the rotten ones for Rs 78 per kg and gained 10%. Mrs. Limbu bought 180 kg of oranges initially and 15 kg were not fit for selling. This leaves 180 kg - 15 kg = 165 kg of oranges fit for selling. If she sold these at Rs 78 per kg, the total selling price would be 165 kg x Rs 78/kg = Rs 12870.
Since she gained 10%, we can set up the following equation to find the cost price (CP):
Selling Price (SP) = Cost Price (CP) + 10% of Cost Price (CP)
SP = CP + (10/100) x CP
SP = 1.1 x CP
Therefore, we can calculate the cost price as follows:
CP = SP / 1.1
CP = Rs 12870 / 1.1
CP = Rs 11700
Now, to find the cost price per kg of oranges, we divide the total cost price by the number of kilograms of oranges that were fit for selling:
Cost Price per kg = Total Cost Price / Number of kilograms sold
Cost Price per kg = Rs 11700 / 165 kg
Cost Price per kg = Rs 70.909...
Since the cost price must match one of the given options, the correct answer is Rs 70 per kg (Option A).