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A tradesman gives 4% discount on his marked price and gives 1 article free for buying every 15 articles and thus gains 35%. By what percent is the marked price increased above the cost price?

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50%

40%

60%

80%

answer is A.

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Detailed Solution

Given that discount is provided of

4 %

and 1 article is given free on buying 15 articles. The gain is

35 %

.
Let the C.P. of each article be Rs. x.
Then C.P. of 16 articles = Rs.16x.
S.P. of 15 articles = 135% of Rs.16x

\Rightarrow

S.P. of 15 articles

=

Rs.

(\frac{135 \times 16 x}{100})

\Rightarrow

S.P. of 15 articles

= Rs . \frac{108 x}{5}

S.P. of 1 article

= Rs . (\frac{108 x}{5} \times \frac{1}{15})

\Rightarrow

S.P. of 1 article

= Rs . \frac{36 x}{25}

Let M.P. = Rs.100.
Then S.P. = Rs.96 after a discount of 4%.

∴

If S.P. is Rs.96 then M.P. = Rs.100
If S.P. is Rs.

\frac{36 x}{25}

then M.P.

= Rs . (\frac{100}{96} \times \frac{36 x}{25})

\Rightarrow

M.P.

= Rs . \frac{4 \times 36}{96}

\Rightarrow

M.P.

= Rs . \frac{3 x}{2}

∴

% Increase in M.P. over C.P.

= \frac{\frac{3 x}{2} - x}{x} \times 100

\Rightarrow

Increase in M.P. over C.P.

= (\frac{x}{2} \times \frac{1}{x} \times 100) %

\Rightarrow

Increase in M.P. over C.P.

= 50 %

So, marked price is increased by

50 %

.
Hence, the correct option is 1.

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