A wholesaler sold a radio to a retailer making a profit of 20%. The retailer later sold the radio for Ksh 1560 making a profit of 30%. Calculate the amount of money the wholesaler had paid for the radio.
wholesaler cost = w
retailer cost = 1.20w
retail price = 1.20w*1.30 = 1.56w
so, 1.56w = 1560
...
1444
To calculate the amount of money the wholesaler had paid for the radio, we can break down the problem into two parts:
1. Calculating the retailer's selling price to determine the cost price to the retailer.
2. Using the retailer's cost price to calculate the wholesaler's cost price.
Let's start with the first step:
Step 1: Calculating the retailer's selling price
The retailer sold the radio for Ksh 1560, making a profit of 30%. To determine the cost price to the retailer, we need to find the original selling price (100%) and subtract the profit percentage (30%).
Profit Percentage = 30%
Selling Price = Ksh 1560
Let's denote the cost price to the retailer as CP_retailer. Using the formula:
Selling Price = Cost Price + Profit
Ksh 1560 = CP_retailer + (30/100) * CP_retailer
Simplifying the equation:
Ksh 1560 = CP_retailer + 0.3 * CP_retailer
Ksh 1560 = 1.3 * CP_retailer
Dividing both sides by 1.3, we get:
CP_retailer = Ksh 1560 / 1.3
CP_retailer = Ksh 1200
So, the cost price to the retailer (CP_retailer) is Ksh 1200.
Now, let's move on to the second step:
Step 2: Calculating the wholesaler's cost price
The wholesaler sold the radio to the retailer with a profit of 20%. To find the wholesaler's cost price, we need to determine the cost price to the retailer (CP_retailer) and work backward.
Profit Percentage = 20%
Cost Price to the retailer (CP_retailer) = Ksh 1200
Let's denote the wholesaler's cost price as CP_wholesaler. Using the formula:
Selling Price = Cost Price + Profit
CP_retailer = CP_wholesaler + (20/100) * CP_wholesaler
Simplifying the equation:
Ksh 1200 = CP_wholesaler + 0.2 * CP_wholesaler
Ksh 1200 = 1.2 * CP_wholesaler
Dividing both sides by 1.2, we get:
CP_wholesaler = Ksh 1200 / 1.2
CP_wholesaler = Ksh 1000
Therefore, the amount of money the wholesaler had paid for the radio is Ksh 1000.