Question

The Simple interest on a certain sum is 16/25 of the sum. Find the rate percent and the time if both are numerically equal

Answer 1

Answer:

Step-by-step explanation:

Let the sum/principal be x.

Given that Simple interest on a certain sum is 16/25 of the sum.

SI = 16/25 * x

   = 16x/25.

Now,

Given that Rate and Time are numerically Equal.

Let the rate of interest and Time be R years.

We know that SI = PTR/100

16x/25 = x * R * R/100

16x/25 = xR^2/100

16/25 = R^2/100

1600 = 25R^2

1600/25 = R^2

64 = R^2

R = 8.

Therefore the Rate = 8%

Time = 8 years

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Answer 2

Answer:

The rate percent and time are 8% and 8 years

Step-by-step explanation:

Let the sum be x

Simple interest = 16x/25

Let the rate of interest be y

We are given that the rate percent and time if both are numerically equal

So, Time = y

So, SI. = (PTR)/100

16/25x = (x x y x y)/100

16/25 = y²/100

√16/25 x 100 = y

8=y

Hence the rate percent and time are 8% and 8 years