A shopkeeper using a faulty weight while professes to sell the article at cost price and gains a profit of 25%. Find the faulty weight he uses for 1000 g.

Correct option is C

Given:

The shopkeeper gains 25% profit by using a false weight.

The professed selling price is at cost price, i.e., he sells at the cost price of 1 kg.

Concept Used:

Let the actual weight used by the shopkeeper for 1 kg be 'x'.

The shopkeeper sells at the cost price of 1 kg, but he gains 25%.

Formula Used:

Selling price = Cost price × (1 + Profit%)

Solution:

Let the cost price of 1 kg be ₹1. The selling price will then be ₹1 × (1 + 0.25) = ₹1.25

He uses 'x' kg of goods to sell at the price of 1 kg (₹1.25). So, he gains 25%.

Now,  

SP = false weight × CP 

1.25 = x × 1

=> x = 1 / 1.25 = 0.8

Thus, for 1 kg, the shopkeeper uses 0.8 kg.

Answer: 800 gm
Alternate Solution:

False weight = $$\frac{\text{Actual weight}}{1 + \text{Gain percentage}}$$​​

Applying the formula; 

False weight = $$\frac{1000}{1.25}$$​

False weight = $$\frac{1000}{1.25}$$ = 800gm