a trader sold 20% of his stock at 10% profit and 50% of the reminder of his stock at 10% loss.What should be the rate of profit for sale of the reminder of stock in order that the trader may make an overall profit of 5% over his entire stock?
Answers
Answer:
The profit % on remaining stock should be 26.67 %.
Step-by-step explanation:
Let the cost of total stock with the trader be x.
Stock sold at profit = 20 % x = 0.2 x
Profit = 10 %
Selling price = 0.2 x + 10 % (0.2 x)
SP = 0.2 x + 0.02 x = 0.22 x
Stock sold at loss = 50 5 x = 0.5 x
Loss = 10 %
SP = 0.5 x - 10 % (0.5 x)
SP = 0.5 x - 0.05 x
SP = 0.45 x.
Total stock sold = 0.2 x + 0.5 x = 0.7 x
Total SP = 0.22 x + 0.45 x = 0.67 x
Remaining stock = x - 0.7 x = 0.3 x
Overall profit that he needs to make = 5 %
Overall SP = x + 5% x = x + 0.05 x = 1.05 x
SP for remaining stock should be = 1.05 x - 0.67 x = 0.38 x
Profit on remaining stock should be = 0.38 x - 0.3 x = 0.08 x
Profit % on remaining stock = (0.08 x / 0.3 x) × 100
Profit % on remaining stock = 26.67 %.
Therefore, the profit % on remaining stock should be 26.67 %.
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