A shopkeeper buys 1800 kg wheat for ₹32,400. If 20% of this wheat is spoiled due to rain, at what rate (₹/kg) should he sell the rest to earn 20%?

Correct Option: 27

Step-by-Step Solution:

Step 1: Calculate the total cost price (CP)
The total quantity of wheat bought = 1800 kg
Total Cost Price (CP) = ₹32,400

Step 2: Find the remaining quantity of wheat after spoilage
Percentage of wheat spoiled = 20%
Amount of wheat spoiled = 20% of 1800 kg
$=\frac{20}{100}\times 1800=360\text{kg}$

Remaining wheat available for sale = Total wheat - Spoiled wheat
$=1800-360=1440\text{kg}$

Step 3: Calculate the total desired Selling Price (SP)
The shopkeeper wants to earn a profit of 20% on his overall investment.
Desired Profit = 20% of Cost Price (CP)
Total Selling Price (SP) = CP + Profit
$=32400+\left(\frac{20}{100}\times 32400\right)$

$=32400+6480=\text{₹}\mathrm{38,880}$

Step 4: Find the selling rate per kg for the remaining wheat
Selling rate per kg = Total Selling Price / Remaining quantity of wheat
$=\frac{38880}{1440}=\text{₹}27\text{per kg}$

Hence, the shopkeeper should sell the remaining wheat at ₹27/kg to earn a total profit of 20%.