# Question 6725f

Feb 24, 2018

The marked price is above the cost price by 50%

#### Explanation:

Let cost price be $C . P . = 100$ for one item.---(1)

Let Marked Price be $M . P .$ for one item.

The tradesman gives 4% discount on the marked price,
That means selling price $S . P = M . P . - \frac{4}{100} \times M . P .$

$S . P . = M . P . \left(1 - 0.04\right) = 0.96 M . P .$---- for one item.

$S . P . = 0.96 M . P .$----------equation.(2)

He gives 1 article free for buying every 15 articles

That means when he sells 16 items for Selling Price of 15 items.

Cost price for 16 items will be :

$C . {P}_{16} = 1600$

$S . {P}_{16} = 15 \times S . P . = 15 \times 0.96 M . P .$ -----substituting from(2)

$\therefore S . {P}_{16} = 14.4 M . P .$ ---------equation.(3)

Profit $P = S . {P}_{16.} - C . {P}_{16.}$

$P = S . {P}_{16.} - 1600$

$P = 14.4 M . P . - 1600$----(4) substituting from (3)

He gains 35% ,

 %P = 35%  ----given.

 %P = P/(C.P_16.) xx 100

therefore %P = P/(1600) xx 100#

$\implies 35 = \frac{P}{1600} \times 100$

$\implies P = \frac{35 \times 1600}{100} = 560$ ----(5)

equating (4) and (5):

$14.4 M . P . - 1600 = 560$

$14.4 M . P . = 560 + 1600$

$M . P . = \frac{2160}{14.4} = 150$

$M . P . = 150$ ----- for each item.

We had $C . P . = 100$

So, the marked price is 50% more than the cost price.

The marked price is above the cost price by= $50$

That means, the trader buys each item for $100, marks them$150 each and sells them at $144 (after 4% discount). He sells 16 items for selling price of 15. So instead of charging$2304 for 16 items, he charges $2160 for 16 items, and gains ($ 560) i.e. 35 % of the cost price.