Question

10. John borrowed some money at the rate of 7% per annum for the first 3yr, at the rate of 9% per annum
for the next 5yr and at the rate of 12% per annum for the period beyond Syr. If he pays a total interest of Rs. 5100
at the end of 11yr. how much money did he borrow?​

Answer 1

Given: John borrowed some money at a rate of $7$% for the first $3$ years, at the rate of $9$% per annum for the next $5$ years, and at the rate of $12$% per annum for the period beyond $8$ years.

John pays a total interest of $5100$ at the end of $11$ years.

To find: The money that John borrowed.

Solution:

Let the money which John borrowed be $x$

When John borrowed Rs $x$ for the first $3$ years is the interest is,

$=\frac{x*3*7}{100}$

When John borrowed the same for the next 5 years at an interest of $9$% the interest is,

$=\frac{x*9*5}{100}$

When the rate is $12$% and the time beyond $8$ years, the interest is,

$=\frac{x*12*3}{100}$  (the time here is $11-8=3$ years)

According to the question,

$\frac{x*3*7}{100}$ + $\frac{x*9*5}{100}$ + $\frac{x*12*3}{100}$ $=5100$

⇒ $\frac{21x}{100}+\frac{45x}{100}+\frac{36x}{100}=5100$

⇒ $\frac{21x+45x+36x}{100}=5100$

⇒ $\frac{102x}{100}=5100$

⇒ $x=\frac{5100*100}{102}$

⇒ $x = 5000$

Final answer:

The money that John borrowed is Rs $5000$