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%.