Question

A 55% decrease followed by a 25% increase A 75% increase followed by a 3313% decrease A 20% decrease followed by a 40% increase A $30 increase followed by a $30 decrease A 100% increase followed by a 50% decrease

Answer 1

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Answer 2

Part 1: Less.

Part 2: Greater.

Part 3: Greater.

Part 4: Less.

Part 5: Equal.

Explanation:

Part 1: Assume that the value is x initially.

So, 55% decrease of value of x will give
`x(1 - (55)/(100)) = 0.45x`.

Again, 25% increase of the value obtained will give
`0.45x(1 + (25)/(100)) = 0.45 * 1.25 * x = 0.5625x`

So, it is less than x. (Answer)

Part 2: Assume that the value is x initially.

So, 75% increase followed by
`33(1)/(3)  = 33.33`% decrease will give
`x * (1 + 0.75) * (1 - 0.333) = x * 1.75 * 0.667 = 1.167x`

So, it is greater than x.

Part 3: Assume that the value is x initially.

So, 20% decrease followed by 40% increase will give
`x * (1 - 0.2) * (1 + 0.4) = x * 0.8 * 1.4 = 1.12x`

So, it is greater than x.

Part 4: Assume that the value is x initially.

So, 30% increase followed by 30% decrease will give
`x * (1 + 0.3) * (1 - 0.3) = x * 1.3 * 0.7 = 0.91x`

Hence, it is less than x.

Part 5: Assume that the value is x initially.

So, 100% increase followed by 50% decrease will give
`x* (1 + 1) * (1 - 0.5) =x * 2 * 0.5 = x`

Hence, the final value is same as x. (Answer)