A shopkeeper promises to sell his goods at x% profit, but he uses a weight 20% less than the true weight and gains \(37\frac{1}{2}\)% in all. Find x.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10%
With a short weight the shopkeeper charges for the full weight but gives only part of it. His real gain compares what he charges with the cost of the goods he actually hands over.
Let the cost price of 1 kg be Rs 100
For “1 kg” he charges \(100+x\) rupees
He actually gives \(0.8\) kg, which costs him Rs 80
Real gain \(=37\frac{1}{2}\%\), so \(\displaystyle 100+x=80\times\frac{137.5}{100}=110\)
\(x=110-100=10\)
The promised profit is 10%.