Question

The simple interest in 3 years and compound interest in 2 years on a certain sum of money at the same rate are Rs. 1200 and Rs. 832 respectively. The principal is?
A) Rs. 7500 B)Rs. 4000 C) Rs. 3000 D)Rs.5000

Answer 1

Hint: The above problem could be solved very easily on the basis of the formula of simple interest and compound interest by directly substituting the values of the variables used in the formula, from the given question , in order to get our result. The formula which we used here are:-
SI = $\dfrac{{P \times R \times T}}{{100}}$
CI = $P{\left( {1 + \dfrac{R}{{100}}} \right)^r}$

Complete step-by-step answer:
Let the principle be Rs 'P' and the rate of interest be R% per annum.
i.)Simple interest of 3 years = Rs 1200
$\therefore $ simple interest for each years = Rs$\dfrac{{1200}}{3}$
Compound interest for the 1st years
= SI of 1 year = Rs 400
Interest for second years = Rs 832 - 400
                   =Rs. 432.
Difference b/w CI and SI for 2nd year
= Rs 432 - 400 = Rs 32.
$\therefore $ R% of 400 = Rs 32
$ \Rightarrow \dfrac{R}{{100}} \times 400 = 32$
$ \Rightarrow R = \dfrac{{32}}{4} = 8\% $ per annum.
ii) $SI = \dfrac{{principal \times rate \times time}}{{100}}$
$ \Rightarrow 1200 = \dfrac{{P \times R \times T}}{{100}} = \dfrac{{P \times 3 \times 8}}{{100}}$
$ \Rightarrow P = Rs.\dfrac{{1200 \times 100}}{{8 \times 3}} = Rs.5000$
iii) CI for 3 years:-
A = $P{\left( {1 + \dfrac{R}{{100}}} \right)^r} = 5000{\left( {1 + \dfrac{8}{{100}}} \right)^3}$
=$5000 \times \dfrac{{108}}{{100}} \times \dfrac{{108}}{{100}} \times \dfrac{{108}}{{100}}$
= 6298.96
So, CI = A – P
$\therefore $ CI = 6298.56 - 5000
= Rs 1298.56
Difference between the CI and SI for 3 years
=Rs (1298.56 - 1200)
=Rs 98.56.
Therefore, option (d) is the correct answer for this particular question.

Note: The formula for the simple interest is given by the following:-
SI = $\dfrac{{P \times R \times T}}{{100}}$where,
P= Principal ; R= Rate of Interest; T= Time of interest of the amount.
The formula for the compound interest is given by the following:-
CI = $P{\left( {1 + \dfrac{R}{{100}}} \right)^r}$
There is also one more formula for compound interest:- A = CI + P
where, P= Principal ; R= Rate of Interest; n=Time (in years); A= Amount;
CI= Compound Interest
 The above formula: A = CI + P will give us the total amount. To get the Compound Interest only, we need to subtract the Principal from the Amount.