A tradesman gives $4 %$ discount on the marked price and gives $1$ article free for buying every $15$ articles and thus gains $35 % .$ The marked price is above the cost price by

20 %

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50 %

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39 %

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40 %

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Solution

The correct option is B $50 %$
Let the C.P. of each article be Rs. $x .$
Then, C.P. of $16$ articles $=$ Rs. $16 x$
S.P. of $15$ articles
$=$ Rs. $16 x \times \frac{135}{100}$
$=$ Rs. $21.6 x$
S.P. of each article
$=$ Rs. $\frac{21.6 x}{15} = 1.44 x$
If S.P. is Rs. $96,$ then marked price $=$ Rs. $100$
If S.P. is Rs. $1.44 x$ , then marked price
$= \frac{100}{96} \times 1.44 x = 1.5 x$
$\Rightarrow$ Marked price $= x + 0.5 x$
$∴$ Marked price $= 50 %$ above C.P.

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A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is above the cost price by

A tradesman gives $4 %$ discount on the marked price and gives $1$ article free for buying every $15$ articles and thus gains $35 % .$ The marked price is above the cost price by