Question

The simple interest on a certain sum amounts to 5/8 of the whole sum at the end of 12 years and 6 months. find the rate percent per annum.

Answer 1

Let the sum of Money = P
SI = 3/8 P
time = 25/4 years
R = ?

SI = PTR/100
⇒ 3/8 P = P × 25/4 × R / 100
⇒ 3/8 = 25R/400
⇒ R = (3×400)/(8×25)
⇒ R = 6%

Answer 2

The simple interest on a certain sum amounts to 5/8 of the whole sum at the end of 12 years and 6 months. Then rate of interest is 5 % per annum

Solution:

Let "p" be the sum

Given that,

The simple interest on a certain sum amounts to 5/8 of the whole sum

Therefore,

$Simple\ Interest = \frac{5}{8} \times p$

Time duration = 12 years 6 months = $12 + \frac{6}{12} = 12.5\ year$

To find: rate of interest per annum

The simple interest is given by formula:

$Simple\ Interest = \frac{ p \times n \times r }{100}$

Where,

p is the principal

n is number of years

r is rate of interest

Therefore,

$\frac{5}{8} \times p = \frac{p \times 12.5 \times r}{100}\\\\r = \frac{ 5 \times 100 }{8 \times 12.5}\\\\r = 5$

Thus rate of interest is 5 % per annum

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