A shopkeeper who professes to sell his goods at cost price, uses a faulty balance that has one arm 4% longer than the other. Is it possible to determine his profit percentage? If yes, then how?
Thanks,
A shopkeeper who professes to sell his goods at cost price, uses a faulty balance that has one arm 4% longer than the other. Is it possible to determine his profit percentage? If yes, then how?
Thanks,
In case the obvious answer is not as obvious as it seems, we do a very detailed calculation.
For definiteness, assume that the cost to the shopkeeper of $1$ gram of the substance is $50$ dollars, and therefore the selling price is $50$ dollars per (short) "gram." The shopkeeper places a $1$ gram weight at the end of the short arm of the balance. Then (s)he delicately places some of the substance into a pan at the end of the long arm, until the balance balances.
Let $w$ be the actual weight of substance in the pan, and let $a$ be the length of the short arm of the balance. Then the long arm has length $1.04a$, so $(1.04a)(w)=(a)(1),$ and therefore $w=\dfrac{1}{1.04}$.
The cost to the shopkeeper of what (s)he sells for $50$ dollars is therefore $\dfrac{50}{1.04}$. The selling price is $50$, so the selling price divided by the cost is $\frac{50}{\frac{50}{1.04}}.$ This ratio is $1.04$, so the profit percentage is $4\%$.