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A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a sticky bargainer. How much percent above the cost price were his wares marked?

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50%

60%

75%

100%

answer is D.

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Detailed Solution

Given,
Discount = 20%
Profit percentage = 20%
Suppose, cost price of a dozen of the item = x
Marked price of a dozen of the item =y
So, cost of 16 article,

= 16 \times \frac{x}{12}

= \frac{4 x}{3}

Marked price of 16 articles,

= 16 \times \frac{y}{12}

= \frac{4}{3} y

Now, total discount,
= 20% of the dozen marked price + four article marked price

= \frac{20}{100} \times y + (16 - 12) \frac{y}{12}

= \frac{y}{5} + \frac{4 y}{12}

= \frac{y}{5} + \frac{y}{3}

Now,
Selling price = 20% of cost price + cost price

Selling price = \frac{20}{100} \times \frac{4}{3} x + \frac{4}{3} x

= 1.2 \times \frac{4}{3} x

= 1.6 x

It is known that,
Selling price = Price marked – discount

\Rightarrow 1.6 x = \frac{4}{3} y - \frac{y}{5} - \frac{y}{3}

\Rightarrow \frac{16 x}{10} = y (\frac{4}{3} - \frac{1}{3} - \frac{1}{5})

\Rightarrow \frac{16 x}{10} = \frac{12 y}{15}

\Rightarrow \frac{240 x}{120} = y

…..(i)
So, percent above the cost price were his wares marked

= \frac{marked price - cost price}{cost price} \times 100

= \frac{\frac{4}{3} y - \frac{4 x}{3}}{\frac{4 x}{3}} \times 100

…….. (ii)
Put the value of y from equation (i) into equation (ii),

= \frac{\frac{4}{3} (\frac{240}{120} - 1)}{\frac{4}{3}} \times 100

= (2 - 1) \times 100 = 100

Thus, the dealer has marked up the price by 100% over his cost price.
Option 4 is correct.

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