Q154
ArithmeticPercentage, Profit & Loss
A dishonest dealer defrauds his seller and buyer by using forged weights to the extent of 20%. His true gain per cent is
- a.20%
- b.40%
- c.44%
- d.50%
Answer: (C) 44%
Standard rule: a dealer who cheats to the extent of $x$ per cent both while buying and while selling makes two successive gains of $x$ per cent, so gain $= x+x+\tfrac{x^2}{100}$. With $x = 20$: $20+20+\tfrac{400}{100} = 44$ per cent. In figures: for a payment of 100 he receives goods worth 120, and he then sells these 120 as if they were $120\times1.2 = 144$. The same formula, $\tfrac{(100+x)^2}{100}-100$, gives 21 per cent when the cheating is 10 per cent.