A dishonest dealer sells his goods at the cost price but still earns a profit of 28% by under weighing. What weight does he use for a kg?

A 750 g

B 800 g

C 825 g

D 781.25 g

E 965.5 g

Correct Answer: Option D

Let’s assume that the dishonest dealer uses a weight of x kg for weighing 1 kg.

Clearly x < 1.

Also, let the cost price of 1 kg of goods be Rs. y.

As per the given information, he sells x kg of goods for Rs. y and gains a profit of 28%.

Selling price of x kg of goods = Rs. y

Selling price of 1 kg of good = y/x

Profit % \(= {{S.P.\; - C.P.} \over {C.P.}} \times 100\)

28 \(= {{\;{y \over x}\; - \;y\;} \over y} \times 100\)

1.28y = y/x

x = 1/1.28 kg

⇒ x = 0.78175 kg = 781.75 g