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Ram bought pens from a wholesaler at Rs. 200 per pen. For every additional pen sold by Ram after the first one, the selling price of the pen becomes Rs.5 less than the selling price of the previous pen. Using this strategy, Ram makes a 145% profit by selling 5 pens. What is the maximum number of pens a customer can buy in a single transaction such that Ram makes a profit on every pen sold?
Verified Answer
Ram bought pens from a wholesaler at Rs. 200 per pen. For every additi...
Let X be the selling price of the first pen.
The selling price of the second pen is X-5.
The selling price of the third pen is X-5-5 = X-10.
The selling price of the fourth pen is X-10-5 = X-15.
The selling price of the fifth pen is X-15-5 = X-20.
The total cost price of the pens is 5200 = 1000.
The total selling price of the pens is X+(X-5)+(X-10)+(X-15)+(X-20) = 5X-50.
The profit made by selling 5 pens is 145% of the cost price of the pens.
This means that the total selling price of the pens is 1.451000 = 1450.
Substituting this value into the expression for the total selling price of the pens, we get 1450 = 5X-50.
Solving for X, we get X=350.
The selling price of the first pen is 350.
Since the selling price decreases by 5 for every additional pen sold, the maximum number of pens a customer can buy in a single transaction such that Ram makes a profit on every pen sold is 6.
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Ram bought pens from a wholesaler at Rs. 200 per pen. For every additi...
Problem: What is the maximum number of pens a customer can buy in a single transaction such that Ram makes a profit on every pen sold?

Given:
- Cost price of each pen = Rs. 200
- Selling price of each additional pen = Rs. 5 less than the selling price of the previous pen
- Ram makes 145% profit by selling 5 pens

To Find: Maximum number of pens a customer can buy in a single transaction such that Ram makes a profit on every pen sold

Solution:
Let's assume that Ram sells x pens in a single transaction.

Calculating Selling Price:
- Selling price of the first pen = Cost price + Profit = 200 + (200 x 145%) = 490
- Selling price of the second pen = 490 - 5 = 485
- Selling price of the third pen = 485 - 5 = 480
- Similarly, selling price of the fourth and fifth pens = 475 and 470

Calculating Total Revenue:
- Total revenue = (490 + 485 + 480 + 475 + 470) = 2,400 + (x-5) x (selling price of the fifth pen - 5)
- Total cost = 200x

Calculating Profit:
- Profit = Total revenue - Total cost
- Profit = [2,400 + (x-5) x (470)] - (200x)
- Profit = 850x - 4,150

For Ram to make a profit on every pen sold, Profit per pen should be positive.
- Profit per pen = Profit / x
- Profit per pen = (850x - 4,150) / x
- Profit per pen = 850 - (4,150/x)

For Profit per pen to be positive, (4,150/x) < />
- x > 4,150/850
- x > 4.88

Conclusion:
Ram can sell a maximum of 4 pens in a single transaction to make a profit on every pen sold. If Ram sells more than 4 pens, he will incur a loss on the additional pens sold.
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Ram bought pens from a wholesaler at Rs. 200 per pen. For every additional pen sold by Ram after the first one, the selling price of the pen becomes Rs.5 less than the selling price of the previous pen. Using this strategy, Ram makes a 145% profit by selling 5 pens. What is the maximum number of pens a customer can buy in a single transaction such that Ram makes a profit on every pen sold?
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