The ratio of the selling prices of three items X, Y and Z is 7 : 8 : 9. The ratio of the numbers of items of X, Y and Z that were sold is 4 : 5 : 6. The difference between the sales revenue from the sale of items X and Z is ₹7,800. Find the total sales value of the three items
Question
The ratio of the selling prices of three items X, Y and Z is 7 : 8 : 9. The ratio of the numbers of items of X, Y and Z that were sold is 4 : 5 : 6. The difference between the sales revenue from the sale of items X and Z is ₹7,800. Find the total sales value of the three items
Solution
Sure, let's solve this step by step.
Step 1: Understand the problem The problem gives us two ratios. The first ratio is the selling prices of three items X, Y, and Z which is 7:8:9. The second ratio is the number of items of X, Y, and Z sold which is 4:5:6. We are also given that the difference between the sales revenue from the sale of items X and Z is ₹7,800.
Step 2: Set up the equations Let's denote the selling price of X, Y, and Z as 7p, 8p, and 9p respectively. Similarly, let's denote the number of items of X, Y, and Z sold as 4n, 5n, and 6n respectively.
The sales revenue from the sale of items X and Z can be calculated as the selling price times the number of items sold. Therefore, we have:
Sales revenue from X = 7p * 4n = 28pn Sales revenue from Z = 9p * 6n = 54pn
We are given that the difference between the sales revenue from the sale of items X and Z is ₹7,800. Therefore, we can set up the following equation:
54pn - 28pn = 7800 26pn = 7800
Step 3: Solve the equation From the equation above, we can solve for pn:
pn = 7800 / 26 = 300
Step 4: Calculate the total sales value The total sales value of the three items can be calculated as the sum of the sales revenue from the sale of each item:
Total sales value = Sales revenue from X + Sales revenue from Y + Sales revenue from Z = 28pn + 40pn + 54pn = 122pn
Substitute pn = 300 into the equation above, we get:
Total sales value = 122 * 300 = ₹36,600
Therefore, the total sales value of the three items is ₹36,600.
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