Question

A sum of money put at 9% per annum simple interest amounts to Rs. 10160 in 3 years. What will it amount to in 2 years at 8% per annum?

Answer 1

Hint – In this particular type of question use the concept that simple interest is the product of the principal amount, time in years and rate of interest divided by 100 and total amount is the sum of principal amount and simple interest so use this concept to reach the solution of the question.

Complete step-by-step answer:
Given data:
Rate of interest (i.e. r) = 9% per annum simple interest.
In 3 years (i.e. t = 3 years) it will amount to 10160 Rs. (i.e. A = 10160 Rs.)
Let the principal value be P Rs.
Now as we know that simple interest (S.I) is the product of the principal amount (P), time in years (t) and rate (r) of interest divided by 100.
Therefore, $S.I = \dfrac{{prt}}{{100}}$
And the amount (A) in a particular time is the sum of the principal value and the simple interest calculated in that time period.
Therefore, A = P + S.I
Now substitute the values in the above equation we have,
$ \Rightarrow 10160 = P + \dfrac{{P.9.3}}{{100}}$
$ \Rightarrow 10160 = P + 27\dfrac{P}{{100}} = \dfrac{{127}}{{100}}P$
$ \Rightarrow P = \dfrac{{10160\left( {100} \right)}}{{127}} = 8000$ Rs.
Now we have to calculate the amount in 2 years (i.e. t’ = 2 years) at 8% (i.e. r’ = 8%) per annum.
Therefore amount (A’) = P + (Pr’t’/100)
Now substitute the values in the above equation we have,
Therefore amount (A’) = $8000 + \dfrac{{8000\left( 8 \right)\left( 2 \right)}}{{100}}$
Now simplify this we have,
Therefore amount (A’) = $8000 + 80\left( {16} \right) = 8000 + 1280 = 9280$ Rs.
So this is the required answer.

Note – Whenever we face such types of questions first of all calculate the principal value use the formula of simple interest and the formula of amount which is all written above then use this principal value to calculate the amount for another case as above and simplify we will get the required answer.