A trader bought the number of articles for Rs. 900. 5 articles were found to be damaged. He sold each of the remaining articles at Rs. 2 more that what he paid for it and got a profit of Rs. 80 as whole transaction. Find the no:of:articles
Answers
Answer:
75
Step-by-step explanation:
STEP 1: Define x:
Let x be the number of articles bought
Number of damaged articles = 5
Number of good articles = x - 5
STEP 2: Find the cost of 1 article:
x articles = Rs 900
1 article = 900 ÷ x = 900/x
STEP 3: Find the selling price of 1 article:
Selling Price = 2 more than the cost price
Selling Price = 900/x + 2
STEP 4: Find the selling price of the (x - 5) articles:
1 article = 900/x + 2
(x - 5) articles = (x - 5)(900/x + 2)
STEP 5: Find the profit in term of x:
Profit = Selling Price - Cost Price
Profit = (x - 5)(900/x + 2) - 900
STEP 6: Solve x:
The profit is Rs 80
(x - 5)(900/x + 2) - 900 = 80
(x - 5)(900/x + 2) = 980
900 + 2x - 4500/x - 10 = 980
2x - 4500/x - 90 = 0
2x² - 90x - 4500 = 0
x² - 45x - 2250 = 0
(x - 75)(x + 30) = 0
x = 75 or x = -30 (rejected, since it cannot be negative)
x = 75
Answer: There were 75 articles.