Question

A shopkeeper professes to sell his goods at cost price but uses 800gram weight instead of 100 kg. Thus his gain is
[a] 10%
[b] 15%
[c] 20%
[d] 25%

Answer 1

Hint: Find the gain the shopkeeper earns on 1 kg of his goods. Since gain %age is not quantity dependent the gain %age shopkeeper earns on 1kg of his goods is equal to the gain %age the shopkeeper earns by selling all his goods.

Complete step-by-step answer:

Let the cost price of 1 kg of goods be Rs x.
So, according to the question, the shopkeeper sells 800 gram for Rs x.
Hence the shopkeeper sells 1 gram for Rs $\dfrac{x}{800}$
Hence the shopkeeper sells 1000 gram for Rs $\dfrac{x}{800}\times 1000=\dfrac{5x}{4}$
Gain = Selling price - cost price $=\dfrac{5x}{4}-x=\dfrac{x}{4}$
We know that gain %age $=\dfrac{Gain}{C.P}\times 100$
Hence gain %age = $\dfrac{x}{4x}\times 100%=\dfrac{100}{4}%=25%$
Hence the shopkeeper earns a gain of 25% on his goods.
Hence option [d] is correct.


Note: Alternatively: This solution is more intuitive than the solution provided above.
Let x be the cost price of 1kg of goods and let the shopkeeper sell y kg of his items.
The cost price of y kg of items = xy.
The selling price of y kg of items can be calculated using the unitary method.
The selling price of 800 gram of items $=x$
Hence selling price of 1 gram of items $=\dfrac{x}{800}$
Hence the selling price of y kg = 1000y gram of items $=\dfrac{1000xy}{800}=\dfrac{5xy}{4}$
Gain = S.P - C.P$=\dfrac{5xy}{4}-xy=\dfrac{xy}{4}$
Hence gain %age $=\dfrac{xy}{4xy}\times 100%=25%$
which is the same as obtained above.