Answer:
Part 1: Less.
Part 2: Greater.
Part 3: Greater.
Part 4: Less.
Part 5: Equal.
Step-by-step explanation:
Part 1: Assume that the value is x initially.
So, 55% decrease of value of x will give [tex]x(1 - \frac{55}{100}) = 0.45x[/tex].
Again, 25% increase of the value obtained will give [tex]0.45x(1 + \frac{25}{100}) = 0.45 \times 1.25 \times x = 0.5625x[/tex]
So, it is less than x. (Answer)
Part 2: Assume that the value is x initially.
So, 75% increase followed by [tex]33\dfrac{1}{3} = 33.33[/tex]% decrease will give [tex]x \times (1 + 0.75) \times (1 - 0.333) = x \times 1.75 \times 0.667 = 1.167x[/tex]
So, it is greater than x.
Part 3: Assume that the value is x initially.
So, 20% decrease followed by 40% increase will give [tex]x \times (1 - 0.2) \times (1 + 0.4) = x \times 0.8 \times 1.4 = 1.12x[/tex]
So, it is greater than x.
Part 4: Assume that the value is x initially.
So, 30% increase followed by 30% decrease will give [tex]x \times (1 + 0.3) \times (1 - 0.3) = x \times 1.3 \times 0.7 = 0.91x[/tex]
Hence, it is less than x.
Part 5: Assume that the value is x initially.
So, 100% increase followed by 50% decrease will give [tex]x\times (1 + 1) \times (1 - 0.5) =x \times 2 \times 0.5 = x[/tex]
Hence, the final value is same as x. (Answer)
