Question

A sum of money lent at simple interest
amounts to 17,145 in 3 years and to
*19,575 in 5 years. Find the sum and the
rate of interest.​

Answer 1

Answer:

The sum is Rs.13500 and rate of interest is 9%

Step-by-step explanation:

The sum is Rs.13500 and rate of interest is 9%

Solution:

Let the sum be "p" and rate of interest is "r"

Amount (A) = Principle (P)  + Simple Interest (I)          

So, Simple Interest = Amount - Principal

Given that a sum of money lent at simple interest amounts to rupees 17145 in 3 years and to rupees 19575 in 5 years

From this, we can say,

Amount = 17145 in 3 years:

So, S.I for 3 years = 17145 - p  ---- eqn 1

Amount = 19575 in 5 years:

So, S.I for 5 years = 19575 - p  ----- eqn 2

Subtracting (2) and (1), we get,

S.I for 2 years = 19575 - p -17145 + p

S.I for 2 years = 2430

Now, SI for 1 year =  

Let us calculate S.I for 3 years = 3 x 1215 = 3645

Now put S.I for 3 years = 3645 in eqn1,

3645 = 17145 - p

p = 13500

Hence sum "p" = 13500

Calculation of Rate of interest:

Where,

"p" = principal sum

"r" = rate of interest

"n" = number of years

We know that S.I for 3 years = 3645 and p = 13500

Here n = 3 years

Hence rate of interest = 9%