Question

A sum of money becomes 7/5 of itself in 6 years. Find the rate of interest per annum.

Answer 1

Answer:

6 whole 2/3 % p.a.

Step-by-step explanation:

Let the sum of money or principal be x

Then amount will be 7x/5

S.I. = amount - principal = 7x/5 - x = (7x -5x)/5 = 2x/5

Time = 6 years

We know that,

Rate of interest = {(S.I. * 100)/(principal * time)}% = {(2x/5 * 100)/(x * 6)}% = {40x/6x}% = 20/3 % = 6 whole 2/3 % p.a.

Answer 2

Let the principal be x

7/5 of principal = Amount = 7x/5

Time (T) = 6 years

Amount = Prinipal + Simple interest

7x/5 = x + SI

$\frac{7x}{5} - x = si$

$si = \frac{7x}{5} - \frac{x \times 5}{1 \times 5}$

$si = \frac{7x}{5} - \frac{5x}{5}$

$si = \frac{2x}{5}$

Let the Rate of interest be R

$si = \frac{ptr}{100}$

$\frac{2x}{5} = \frac{x \times 6 \times r}{100}$

$\frac{2x}{5} = \frac{6x \times r}{100}$

By cross multiplication :

$2x(100) = (6xr)5$

$200x = 30xr$

$\frac{200x}{30x} = r$

$r = \frac{20}{3}$

$r = 6 \frac{2}{3}$

Therefore Rate of interest is 6 whole 2/3%.