Question

The simple interest on a certain sum for 4 years at 9% per annum is ₹117 more than the simple interest on the same sum for 3 year at 10% per annum. Find the sum​

Answer 1

Given:

Let P be the principal sum.

As we know that,

$S.I=\frac{P * r * t}{100}$

where S.I.= Simple interest

P= Principal sum

r= Rate

t= time

There are two condition are as follows:

Condition 1:- For 4 years at the rate of 9% per annum.

$S.I=\frac{P*4*9}{100}$          -(1)

condition 2 :- For 3 years at the rate of 10% per annum

$S.I=\frac{P*3*10}{100}$       -(2)

Now according to the question

$\frac{P*4*9}{100}=\frac{P*3*10}{100} + 117$

$\frac{P*36}{100}=\frac{(P*30)+11700}{100}$

36P=30P+11700

36P-30P=11700

6P=11700

P=11700/6

P=1950

Hence The sum is 1950

Answer 2

According to the question we have to determine the sum,

Let P be the principal sum.

As we know that, the formula for simple interest,

$S.I=\frac{P*R*T}{100}$

As there are 2 condition according to the question:-

(i)  For $4$ years at the rate of $9$% per annum.

$=>S.I=\frac{P*4*9}{100}...(1)$

Similarly,

(ii) For $3$ years at the rate of $10$% per annum.

$=>S.I=\frac{P*3*10}{100}...(2)$

According to the question,

From equation (1) and (2),

$=>\frac{P*4*9}{100}=\frac{P*3*10}{100}+117$

On, simplifying the above expression we get,

$=>\frac{P*36}{100}=\frac{(P*30)+11700}{100}$

$=>36P=30P+11700$

By solving like terms,

$=>36P-30P=11700\\=>6P=11700\\=>P=1950$

Hence, their sum is $1950$.