A merchant purchased 650kg of wheat at Rs. 50 per kg. He sold 250kg of it at a profit of 24% and 200kg at a loss of 24%. At what rate per kg (in Rs.) should he sell the remaining wheat to gain 20% on his initial investment?

Let's solve this using the overall profit/loss percentage concept.
Total wheat = 650kg

Part 1: 250kg at +24% profit

Part 2: 200kg at −24% loss

Part 3 (Remaining): 650−(250+200)=200kg at let's say x% profit/loss.

The overall desired profit is 20%.
Using weighted average:

250×24+200×(−24)+200×x=650×20
6000−4800+200x=13000
1200+200x=13000
200x=11800
x=59%
So, the remaining 200kg must be sold at a 59% profit.
Cost price per kg = Rs. 50
Selling price per kg for the remaining wheat:

Selling Price=50×(1+
100
59
​
)=50×1.59=79.5