John and Mike had equal amount of money in savings at the beginning of last year. Then Mike’s savings increased by 20% by the end of last year and decreased by 20% this year. John’s savings at first decreased by 20% by the end of last year and then increased by 20% this year. What percentage of John’s and Mike’s savings combined are John’s savings alone?

A. 25% B. 40% C. 50% D. 75% E. 96%

(C) Let’s denote by x amount of money each of them had in savings at the beginning of last year.

Considering changes in Mike’s savings he currently has 1.2 × 0.8 × x = 0.96x Considering changes in John’s savings he currently has 0.8 × 1.2 × x = 0.96x

In order to calculate what percentage of John’s and Mike’s savings combined are John’s savings alone we divide Jon’s savings alone by John’s and Mike’s savings combined: 0.96x / (0.96x + 0.96 x) = 1/2 =0.5 = 50%.

The answer is C. ----------- In this question, the assumption is that the decrease/increase in savings in the beginning of this year were on the original saving amount. Why is it so?

There is NO such assumption. In the explanation we apply increase/decrease simultaneously. Let's consider it in steps.

Let’s denote by x amount of money each of them had in savings at the beginning of last year. Mike’s savings by the end of last year increased by 20%: 1.2x John’s savings by the end of last year decreased by 20%: 0.8x

Mike’s savings decreased by 20% this year: (1.2x) × 0.8 = 0.96x John's savings increased by 20% this year: (0.8x) × 1.2 = 0.96x

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