Question

The simple interest on a sum
of money is 4/9of the principal.
Find the rate percent and time,if both numerically equal.

Answer 1

given that simple interest=4/9th of principle

let the principle be x& rate=time=y;

according to question:

p*r*t/100=4*sum/9

$x \times y {}^{2} \div 100 = 4x \div 9$

$x \times y {}^{2} = 100(4x \div 9)$

$x \times y {}^{2} = 400x \div 9$

$x \times y {}^{2} \div 400x = 9$

cancelling x we get:

$y {}^{2} \div 400 = 9$

$y {}^{2} = 9 \times 400$

$y {}^{2} = 3600 \\ \\ y = 60$

thus,rate=60%and time=60days

now,put the value of y in above equation to get value of x..