If a positive integer $m$ was increased by $20$%, decreased by $25$%, and then increased by $60$%, the resulting number would be what percent of $m$?
A common step-by-step calculation will take time.
After $20$% increase, $6m/5$.
After $25$% decrease, $9m/10$.
After $60$% increase, $144m/100$.
Finally, $m \cdot \frac{x}{100} = \frac{144m}{100} = 144$%
what is the faster (or, fastest) method to solve this?
On
This is what I would put into my calculator: $$ 1.2 \times \underbrace{0.75}_{=1-0.25} \times 1.6 = 1.44 $$
On
There is no shorter method. Only thing you can do to make it short is do all calculations in the end. Log would've worked but it is for only even increases/decreases and for a long period of time
OR
For an alternative take the number as 1, it doesn't change anything except making expression simpler.
The quickest way to do this is to dispense with algebra, and instead of calling your original amount $m$, call it $100$.
A $20\%$ increase turns $100$ into $120$.
A $25\%$ decrease takes off $1/4$ of that, leaving $90$.
A $60\%$ increase adds $6/10$ of $90$, which is $6\times 9$, which is $54$. Thus, $90+54=144$.
Since you started with $100$ and ended with $144$, that's a $44\%$ increase.