Question #6725f

1 Answer
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. - 4/100 xx M.P.

S.P. = M.P. (1- 0.04)= 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 xx S.P. = 15 xx 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 = 14.4M.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

=> 35 = P/ (1600) xx 100

=> P = (35xx 1600)/100= 560 ----(5)

equating (4) and (5):

14.4M.P. - 1600 = 560

14.4 M.P. = 560 + 1600

M.P. = 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.