Since this is a percentage change question that doesn't give us any value, we can take 100 as our base value.Let's say we buy a commodity of 100gm at the cost of $100 (
i.e. $1 per gram).
But now we get 25% extra i.e. on 100gm we get an extra of 25% at the same cost. So now we get 125gms for $100.
On a normal day if we needed 125grm we would have spent $125. But since we only spend $100, we are basically given a discount. Now all we need to do is convert this statement in a mathematical one.
It's like saying, what is the percentage decrease on a bill of $125 if only $100 was paid. (
IanStewart am I correct with this understanding)
So,
Initial Value = $125 (Original price of the commodity of 125gms)
Finial Value = $100 (Actual price paid for the commodity of 100gms)
Using the percentage decrease formula \(\frac{Initial value - Final value}{Initial value} \)\(* 100\) \(= ?\)
\(\frac{125 - 100}{125}\) \(* 100 \) \(= ?\)
= 20%
Tip: Generally there is a relationship between 25% and 20%. If we increase something by 25% we need to decrease the new value by 20% to get the original value back. If we decrease something by 20% we need to increase the new value by 25% to get the original value.
The above tip can be used in this work/rate question:
https://gmatclub.com/forum/it-takes-10- ... 15907.html Notice how statement (1) is actually the same as statement (2)
garcmillan has given a very cool method to go about with it. Learnt something new