A shopkeeper professes to sell his goods at a 5% loss but uses a false balance and gains 40%. The actual weight (rounded off to one decimal place) he uses for 1 kg is:
678.6 gm
Assume the cost price of 1000 g of the good is ₹100, so the cost per gram is ₹0.1.
The shopkeeper claims a 5% loss on the sale of 1 kg, so the selling price for what he calls 1 kg is \(100 - 5 = 95\).
Let the actual weight he delivers for 1 kg be \(W\) grams. His actual cost for this quantity is \(0.1 W\).
He actually gains 40%, so \(95 = 1.4 \times 0.1 W = 0.14 W\).
Solve: \(W = \dfrac{95}{0.14} = \dfrac{9500}{14} \approx 678.57\) g.
Hence, the actual weight used for 1 kg is 678.6 gm.
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