# Incomes of the population increased by 5%, and in a year – by 10%. How much did income increase in total?

Incomes of the population increased by 5%, and in a year – by 10%. How much did income increase in total? The cost of the goods decreased first by 20%, and then by 15%. By what percentage of the total has the cost of the goods decreased?

Let us denote the initial income of the population through x.

Then, after an increase in a year by 5%, the incomes of the population began to be:

x + 1.05x = 1.05x.

After an increase in a year by another 10%, the income of the population began to be:

1.05x + 0.1 * 1.05x = 1.05x + 0.105x = 1.155x.

Consequently, over 2 years, the income of the population increased by:

100 * (1.155x – x) / x = 100 * 0.155x / x = 100 * 0.155 = 15.5%.

Let’s denote the initial cost of the goods through x.

After reducing the price by 20%, the goods began to cost:

x – 0.2x = 0.8x.

After reducing the price by another 15%, the goods began to cost:

0.8x – 0.15 * 0.8x = 0.8x – 0.12x = 0.68x.

Consequently, the total value of the goods decreased by:

100 * (x – 0.68x) / x = 100 * 0.32x / x = 100 * 0.32 = 32%.

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