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The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

Solution

✅ Correct Option: 4

Original cost price = xx rupees

Original selling price = yy rupees


A 40% profit means the selling price is 1.4 times the cost price

Profit = 40% of cost price = 0.4x0.4x rupees

Selling price = Cost price + Profit

Therefore: y=x+0.4x=1.4xy = x + 0.4x = 1.4x


The problem states "product had cost 40% less":

If original cost = xx, then 40% less means we subtract 40% from xx

New cost price = x−0.4x=0.6xx - 0.4x = 0.6x rupees

The selling price is "5 rupees less":

New selling price = y−5=1.4x−5y - 5 = 1.4x - 5 rupees


Profit %=Selling Price−Cost PriceCost Price×100\small \text{Profit \%} = \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100

Since the new profit is 50%:

New SP−New CPNew CP=0.5\dfrac{\text{New SP} - \text{New CP}}{\text{New CP}} = 0.5

(1.4x−5)−0.6x0.6x=0.5\dfrac{(1.4x - 5) - 0.6x}{0.6x} = 0.5

0.8x−50.6x=0.5\dfrac{0.8x - 5}{0.6x} = 0.5


0.8x−5=0.5×0.6x0.8x - 5 = 0.5 \times 0.6x

0.8x−5=0.3x0.8x - 5 = 0.3x

0.8x−0.3x=50.8x - 0.3x = 5

0.5x=50.5x = 5

x=10 rupeesx = 10 \text{ rupees}


Original selling price = 1.4x=1.4×10=141.4x = 1.4 \times 10 = 14 rupees

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