A tradesman fixed the selling prices of goods at $30 %$ above the cost price. he sells half of the stock at this price, one-quarter of his stock at a discount of $15 %$ on the original selling price, and the rest at a discount of $30 %$ on the original selling price. Find the gain per cent altogether.

11 \frac{1}{9}

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13 \frac{7}{9}

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15 \frac{3}{8}

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17 \frac{5}{8}

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Solution

The correct option is C $15 \frac{3}{8}$ %
Lets the cost price $100$ Item each $100$ Rs
Then total cost $= 100 \times 100 = 10000$
Marked selling prices $= 100 + 30 = 130$ Rs
Half item sells same price $= 50 \times 130 = 6500$ Rs
One fourth item on $15 %$ discount $= 25 \times 130 \times 0.85 = 2762.50$ Rs
One fourth item on $30 %$ discount $= 25 \times 130 \times 0.70 = 2275$ Rs
Total selling price $= 6500 + 2762.50 + 2275 = 11537.50$ Rs
Profit on sell $= 11537.50 - 10000 = 1537.50$ Rs
$%$ of Profit $= \frac{1537.50 \times 100}{10000} = 15 \frac{3}{8} %$

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A tradesman fixed the selling prices of goods at 30% above the cost price. he sells half of the stock at this price, one-quarter of his stock at a discount of 15% on the original selling price, and the rest at a discount of 30% on the original selling price. Find the gain per cent altogether.