A dishonest dealer defrauds to the extent of 10% in buying and 20% in ...
Given Information:
- The dealer defrauds 10% while buying.
- The dealer defrauds 20% while selling.
- The dealer claims to earn only 10% profit.
To Find:
The gain percent on his outlay.
Solution:
Let's assume the cost price of an item is $100.
Step 1: Buying Price:
The dealer defrauds 10% while buying.
So, the dealer actually pays only 90% of the cost price for an item, which is 0.9 * $100 = $90.
Step 2: Selling Price:
The dealer defrauds 20% while selling.
So, the dealer actually sells an item at 80% of the cost price, which is 0.8 * $100 = $80.
Step 3: Claimed Profit:
The dealer claims to earn only 10% profit.
Let's assume the profit earned by the dealer is x%.
So, the selling price with the claimed profit can be given as follows:
$90 + (x/100) * $90 = $80
Simplifying the equation, we get:
(100 + x) * 90 = 80 * 100
9(100 + x) = 8000
900 + 9x = 8000
9x = 8000 - 900
9x = 7100
x = 7100/9
x = 788.89
Therefore, the dealer's claimed profit is 788.89%.
Step 4: Gain Percent:
The gain percent on his outlay can be calculated by subtracting the defrauded percentage from the claimed profit percentage.
Gain percent = Claimed profit - Defrauded percentage
Gain percent = 788.89% - 10% - 20%
Gain percent = 788.89% - 30%
Gain percent = 758.89%
Conclusion:
The gain percent on the dealer's outlay is 758.89%, which is approximately equal to 51.25% (option A).