Transaction Analysis

The problem asks us to find the cost price (CP) of the first watch purchased by a man. We know the total cost of two watches, the profit percentage on the first watch, the loss percentage on the second watch, and the overall profit percentage on the entire transaction.

Given Transaction Details

Here's a summary of the provided information:

Calculation Method

We'll use algebraic equations to solve this. Let:

• CP1 = Cost Price of the first watch
• CP2 = Cost Price of the second watch
• SP1 = Selling Price of the first watch
• SP2 = Selling Price of the second watch
• TSP = Total Selling Price

1. Formulating the Equations

Based on the details, we can write:

• Total Cost Price: CP1 + CP2 = 4000 --(Equation 1)
• Selling Price of Watch 1: SP1 = CP1 $\times$ (1 + 20/100) = CP1 $\times$ 1.20
• Selling Price of Watch 2: SP2 = CP2 $\times$ (1 - 10/100) = CP2 $\times$ 0.90
• Total Selling Price: TSP = SP1 + SP2 = (1.20 $\times$ CP1) + (0.90 $\times$ CP2)
• Overall Profit Amount: 5% of 4000 = (5/100) $\times$ 4000 = 200
• Total Selling Price (from overall profit): TSP = Total Cost Price + Overall Profit = 4000 + 200 = 4200

So, the second key equation is:

1.20 $\times$ CP1 + 0.90 $\times$ CP2 = 4200 --(Equation 2)

2. Solving for CP1

We need to solve the system of two equations:

1. CP1 + CP2 = 4000
2. 1.20 $\times$ CP1 + 0.90 $\times$ CP2 = 4200

From Equation 1, express CP2:

CP2 = 4000 - CP1

Substitute this into Equation 2:

1.20 $\times$ CP1 + 0.90 $\times$ (4000 - CP1) = 4200

Distribute the 0.90:

1.20 $\times$ CP1 + 3600 - 0.90 $\times$ CP1 = 4200

Group the CP1 terms:

(1.20 - 0.90) $\times$ CP1 = 4200 - 3600

0.30 $\times$ CP1 = 600

Calculate CP1:

CP1 = $\frac{600}{0.30}

CP1 = 2000

3. Determining the Cost Price of the First Watch

The calculation shows that the cost price of the first watch is Rs. 2000.