the interest paid on each of the three different sums of money yeilding 1%, 2% and 4% simple interest per - Maths - Statistics

Question

the interest paid on each of the three different sums of money
yeilding 1%, 2% and 4% simple interest per annum respectively, is
the same find the average yield percent on the total sum
inverted

Ankush Jain · Accepted Answer

Let the three sums of money be x, y and z yielding 1%, 2% and 4% simple interest per annum respectively.

Given, the simple interest generated on all the three sums are equal.

So, let the simple interest be Rs a.

We know that,

SI = $\frac{P \times R \times T}{100}$

For sum of money Rs x and yield 1%, we have

$a = \frac{x \times 1 \times 1}{100} \Rightarrow x = 100 a ... (1)$

For sum of money Rs y and yield 2%, we have

$a = \frac{y \times 1 \times 2}{100} \Rightarrow y = 50 a ... (2)$

For sum of money Rs z and yield 4%, we have

$a = \frac{z \times 1 \times 4}{100} \Rightarrow z = 25 a ... (3)$

Adding equations (1), (2) and (3), we get

x + y + z = 100a + 50a + 25a

⇒ x + y + z = 175a

Now, average yield percent on the total sum invested = $\frac{t o t a l s i m p l e int e r e s t}{t o t a l s u m} \times 100 = \frac{a + a + a}{x + y + z} \times 100 = \frac{3 a}{175 a} \times 100 = 1.71 %$

the interest paid on each of the three different sums of money yeilding 1%, 2% and 4% simple interest per annum respectively, is the same. find the average yield percent on the total sum inverted.