Question : A dishonest dealer professes to sell his goods at cost price but uses a false weight and thus gains 15%. For a kilogram, he uses a weight of _________ (rounded off to one digit after decimal).
Option 1: 833.3 gm
Option 2: 876.7 gm
Option 3: 869.6 gm
Option 4: 898.33 gm
Correct Answer: 869.6 gm
Solution :
Let the cost price of 1 kg good be Rs. $x$.
Let the weight of faulty weight be $w$ kg.
Selling price of $w$ kg good by unfair means = Rs. $x$
Cost price of $w$ kg good = Rs. $wx$
Profit% = $\frac{\text{Selling price-Cost price}}{\text{Cost price}}\times 100$%
⇒ 15 = $\frac{x-wx}{wx}\times 100$
⇒ $15wx=100x-100wx$
⇒ $115wx = 100x$
⇒ $w=0.8696$ kg
⇒ $w$ = 869.6 gm
Hence, the correct answer is 869.6 gm.
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