A seller marks the price 50% above the cost price and gives a 10% discount on an item. While selling, he cheats the customer by offering 20% less weight. What is the approximate value of the overall profit per cent?

It is given the seller marks the price 50% above the cost price.

Marked Price M.P.=1.5(C.P.)

Also, the seller is giving a discount of 10% on the item.

So, S.P.=0.9(M.P.)=0.9*1.5(C.P.)

Since, S.P.=1.35(C.P.)

So, profit percentage = 35%

However, he also cheats the customer by offering 20% less weight. Therefore, a profit percentage for this part will also be accounted for.

Suppose the seller is claiming that he sells 100 gm of that item, but in reality, he is selling $$100\left(1-\dfrac{20}{100}\right)=80$$ gm.

So, basically he is making a profit of $$(100-80)=20$$ gm

So, profit percentage in this case = $$\dfrac{20}{80}\cdot100=25\%$$

So, overall profit percentage will be = $$0.35+0.25+0.35\times\ 0.25=0.6875=68.75\%$$

Out of the given answer choices, the best approximation is option C, $$68\%$$