Problem Setup

Let $CP_S$ be the cost price (CP) of one Samsung phone and $CP_M$ be the cost price of one Mi phone.

Sarita buys 2 Samsung phones and 3 Mi phones for a total cost of ₹40,200.

This can be written as the equation:

$2 \times CP_S + 3 \times CP_M = 40200 \quad (Equation 1)$

She sells the Samsung phones at a 10% profit and Mi phones at a 20% profit. The total profit is ₹5,640.

Profit from 2 Samsung phones = $10\%$ of $(2 \times CP_S) = 0.10 \times (2 \times CP_S) = 0.20 \times CP_S$.

Profit from 3 Mi phones = $20\%$ of $(3 \times CP_M) = 0.20 \times (3 \times CP_M) = 0.60 \times CP_M$.

The total profit equation is:

$0.20 \times CP_S + 0.60 \times CP_M = 5640 \quad (Equation 2)$

Solving for Mi Phone Cost Price

Multiply Equation 2 by 10 to eliminate decimals:

$10 \times (0.20 \times CP_S + 0.60 \times CP_M) = 10 \times 5640$

$2 \times CP_S + 6 \times CP_M = 56400 \quad (Equation 3)$

Now, subtract Equation 1 from Equation 3:

$ (2 \times CP_S + 6 \times CP_M) - (2 \times CP_S + 3 \times CP_M) = 56400 - 40200 $

$ 2 \times CP_S + 6 \times CP_M - 2 \times CP_S - 3 \times CP_M = 16200 $

$ 3 \times CP_M = 16200 $

Divide by 3 to find the cost price of one Mi phone:

$ CP_M = \frac{16200}{3} $

$ CP_M = 5400 $

The cost price of the Mi phone is ₹5,400.