Question

a sum of money lent at simple interest amounts to rupees 17145 in 3 years and to rupees 19575 in 5 years find the sum and the rate of interest ​

Answer 1

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 = $\frac{2430}{2} = 1215$

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:

$S.I = \frac{P \TIMES N \TIMES R}{100}$

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

$3645 = \frac{13500 \times 3 \times r}{100}\\\\3645 = 135 \times 3 \times r\\\\r = 9$

Hence rate of interest = 9%

Learn more about simple interest

A sum of money lent at simple interest amounts to Rs 4745 in 3 yrs and to Rs 5475 in 5 yrs. find the sum and rate percent per annum.

https://brainly.in/question/1076746

A person deposited ₹4000 in simple interest rate for 2 months. if the gets ₹ 60 as interest what is the rate of interest

https://brainly.in/question/3199299

Answer 2

Answer:

Amount after 2 years =Rs.783

Amount after 3 years =Rs.837

Therefore,

S.I. of 1 year =837−783=Rs.54

⇒ S.I. of 2 years =54×2=Rs.108

Principal sum =783−108=Rs.675

Therefore,

S.I.=

100

PRt

⇒54=

100

675×R×1

⇒R=

675

54×100

=8%