Question

Вкладчик в начале года часть имевшихся у него денег положил в один банк под 60%годовых ,а остальные деньги в другой банк под 40% годовых . через два года суммарное количество денег на обоих счетах удвоилось. какую часть денег вкладчик положил в первый банк? ответ 1/15 . нужно решение))

Answer 1

1/х-часть положил в банк под 60%, (1-1/ч)-часть положил под 40%
1/х *(160/100)²+(1-1/ч)*(140/100)²=2
256/100х +196/100-196/100х=2
256+196х-196=200х
4х=60
х=15
1/15-часть положил в банк под 60%,

Answer 2

Calculation of the Amount in Each Bank Account

To solve this problem, let's assume that the initial amount of money the depositor had was x.

The depositor put a portion of this money into one bank at an interest rate of 60% per year, and the remaining money into another bank at an interest rate of 40% per year.

After two years, the total amount of money in both accounts doubled. Let's calculate the amount in each account after two years.

The amount in the first bank account after two years can be calculated using the formula:

Amount in first bank account after two years = x * (1 + 0.6)^2.

The amount in the second bank account after two years can be calculated using the formula:

Amount in second bank account after two years = x * (1 + 0.4)^2.

Calculation of the Ratio

To find the ratio of the amount of money deposited in the first bank to the total initial amount, we need to divide the amount in the first bank account after two years by the total initial amount.

Let's calculate the ratio:

Ratio = Amount in first bank account after two years / Total initial amount

Substituting the formulas we derived earlier:

Ratio = (x * (1 + 0.6)^2) / x

Simplifying the equation:

Ratio = (1 + 0.6)^2

Calculating the ratio:

Ratio = 1.96

Therefore, the ratio of the amount of money deposited in the first bank to the total initial amount is 1.96.

Calculation of the Fraction

To find the fraction of the money deposited in the first bank, we need to divide the amount of money in the first bank account after two years by the total amount of money in both accounts.

Let's calculate the fraction:

Fraction = Amount in first bank account after two years / (Amount in first bank account after two years + Amount in second bank account after two years)

Substituting the formulas we derived earlier:

Fraction = (x * (1 + 0.6)^2) / ((x * (1 + 0.6)^2) + (x * (1 + 0.4)^2))

Simplifying the equation:

Fraction = (1 + 0.6)^2 / ((1 + 0.6)^2 + (1 + 0.4)^2)

Calculating the fraction:

Fraction = 1.96 / (1.96 + 1.44)

Fraction = 1.96 / 3.4

Fraction = 0.576

Therefore, the fraction of the money deposited in the first bank is approximately 0.576, which can be simplified to 8/14 or 4/7.

So, the depositor put approximately 4/7 of the money in the first bank.

Please note that the calculations provided are based on the assumption that the interest is compounded annually.