The Novak family 2

The Novak family had debts at two banks. They repaid Bank A 26,500 CZK, with interest making up one fifth of the amount. They repaid Bank B an amount 15,000 CZK less, including ten percent interest.

a) What was the Novák family's original debt to Bank A?
b) How much did they originally owe Bank B?
c) What total amount did they pay to both banks? What percentage of it was interest?

Final Answer:

a =  21200 Kc
b =  10454.55 Kc
C =  38000 Kc
p =  16.7 %

Step-by-step explanation:

$$\begin{gathered} A=26500\text{Kc} \\ {u}_1=A/5=26500/5=5300\text{Kc} \\ a=A-u_1=26500-5300=21200\text{Kc} \end{gathered}$$

$$\begin{gathered} B=A-15000=26500-15000=11500\text{Kc} \\ r=100\%+10\%=1+\frac{10}{100}=1.1 \\ b\cdot r=B \\ b=B/r=11500/1.1=10454.55\text{Kc} \end{gathered}$$

$C=A+B=26500+11500=38000\text{Kc}$

$p=100\cdot \frac{C-a-b}{C}=100\cdot \frac{38000-21200-10454.5455}{38000}=16.7\%$

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