Question #6725f

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.