Question : A fruit seller sells $\frac{2}{5}$th part of fruits at a profit of 10% and remaining at a loss of 5%. If the total profit is INR 1850, then what is the total cost price of fruits?
Option 1: INR 198000
Option 2: INR 205000
Option 3: INR 185000
Option 4: INR 176000
Correct Answer: INR 185000
Solution :
Let $x$ be the cost price of fruits.
Profit = 10%
Selling price of $\frac{2}{5}^{th}$ part of fruits = $\frac{2}{5}×x×\frac{110}{100}$ = $0.44x$
Loss = 5%
Selling price of remaining part of fruits = $\frac{3}{5}×x×\frac{95}{100}$ = $0.57x$
Total selling price = $0.44x + 0.57x= 1.01x$
Total profit = INR 1850
According to the question,
$1850 = 0.01x$
$\therefore x = \frac{1850}{0.01} = 185000$
Hence, the correct answer is INR 185000.
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