the ratio of the price of coffee A to coffee B is 2:3. During a certain month, a store sells coffee A and coffee B in the ratio of 4:5. If the total revenue from the sale of these two coffees is Rs27,600, how much of the revenue was from the sale of coffee A?
To solve this problem, we need to break it down into steps:
Step 1: Set up the ratios
Given that the ratio of the price of Coffee A to Coffee B is 2:3, we can assign variables to the prices. Let's say the price of Coffee A is 2x and the price of Coffee B is 3x. This way, the given ratio can be represented as 2x:3x.
Step 2: Set up the second set of ratios
We are told that during a certain month, the store sells Coffee A and Coffee B in the ratio of 4:5. Let's assign variables to the amounts of Coffee A and Coffee B sold. Let's say the quantity of Coffee A sold is 4y and the quantity of Coffee B sold is 5y. The ratio can be represented as 4y:5y.
Step 3: Calculate the total revenue
To calculate the total revenue, we need to multiply the quantity of each type of coffee sold by its respective price and then add them together. Since the total revenue is given as Rs27,600, we can set up the equation:
(Price of Coffee A * Quantity of Coffee A) + (Price of Coffee B * Quantity of Coffee B) = Rs27,600
(2x * 4y) + (3x * 5y) = 27,600
8xy + 15xy = 27,600
23xy = 27,600
Step 4: Solve for xy
To solve for xy, divide both sides of the equation by 23:
xy = 27,600 / 23
xy = 1,200
Step 5: Calculate the revenue from the sale of Coffee A
Now that we have the value of xy, we can calculate the revenue from the sale of Coffee A. Since the price of Coffee A is 2x and the quantity sold is 4y, we can multiply them together:
Revenue from the sale of Coffee A = (Price of Coffee A * Quantity of Coffee A)
Revenue from the sale of Coffee A = (2x * 4y)
Revenue from the sale of Coffee A = 8xy
Revenue from the sale of Coffee A = 8 * 1,200
Revenue from the sale of Coffee A = Rs9,600
Therefore, Rs9,600 of the total revenue of Rs27,600 was from the sale of Coffee A.