Answer:
In 100% increase followed by a 50% decrease,
Final result will be same as the original value,
In option (1) : Final result will be greater than the original value,
In option (2) : Final result will be same as the original value,
In option (3) : Final result will be less than the original value,
In option (4) : Final result will be greater than the original value,
Step-by-step explanation:
Let the original cost = 100,
100% increase followed by a 50% decrease,
Final cost = [tex]100\times (1+\frac{100}{100})(1-\frac{50}{100})[/tex]
[tex]=100\times \frac{200}{100}\times \frac{50}{100}[/tex]
[tex]=\frac{1000000}{100}[/tex]
[tex]=100[/tex]
Thus, original cost = final cost,
75% increase followed by a 33(1/3)% or 100/3% decrease,
Final cost = [tex]100\times (1+\frac{75}{100})(1-\frac{100}{300})[/tex]
[tex]=100\times \frac{175}{100}\times \frac{200}{300}[/tex]
[tex]=\frac{3500000}{30000}[/tex]
[tex]=116.67\%[/tex]
Thus, original cost < final cost,
$30 increase followed by a $30 decrease,
Final cost = 100 + 30 + 30 = 100
Thus, original amount = final cost,
55% decrease followed by a 25% increase,
Final cost = [tex]100\times (1-\frac{55}{100})(1+\frac{25}{100})[/tex]
[tex]=100\times \frac{45}{100}\times \frac{125}{100}[/tex]
[tex]=\frac{562500}{10000}[/tex]
[tex]=56.25[/tex]
Thus, original cost > final cost,
20% decrease followed by a 40% increase,
Final amount = [tex]100\times (1-\frac{20}{100})(1+\frac{40}{100})[/tex]
[tex]=100\times \frac{80}{100}\times \frac{140}{100}[/tex]
[tex]=\frac{1120000}{10000}[/tex]
[tex]=112[/tex]
Thus, original cost < final amount.
