Aptitude - Simple Interest - Discussion

Amount(A) = Principle(p) + Simple Interest(SI).

The sum of money i.e Principle(p) invested or borrowed results an Amount of 815 in 3 years and 854 in 4 years. Since Rate of interest(R) is not mentioned assume it as same for both.

A1 = P + SI1
815 = P + SI1
P = 815 - SI1--- eq1

A2 = P + SI2
854 = P + SI2
P = 854 - SI2 ----- eq2

eq1= eq2
therefore -----> SI2 - SI1 = 854 - 815 =39
Now,
SI1 = P*T1*R/100 =P*3*R/100
SI2 = P*T2*R/100 = P*4*R/100
SI2 - SI1 = P*R/100

39 = P*R/100 -------> Here we can say T=1year, so this is SI for 1 year
now calculate SI for 3 or 4 years
SI for 1 year = 39
SI for 3 years = 39*3 = 117 Which is SI1 or SI for 4 years = 39*4 = 156 which is SI2.

A1 = P + 117
815 = P + 117
P = 815 - 117 = 698


A2 = P + 156
854 = P+156
P = 854 -156 = 698

So sum of money i.e Principle P = 698.

Hi Friends!

Principal = the amount you borrowed.
Interest = the small additional amount you pay for the amount you borrowed.

First let me explain you the question.
In the question,

A sum of money at simple interest amounts to Rs. 815 in 3 years means the Principal amount together with the interest paid for 3 yrs is Rs. 815 and similarly Principal amount together with the interest paid for 4 yrs is Rs. 854

Therefore, if we subtract (854-815) we get the simple interest for 1 year as Rs. 39.

Then, we calculate simple interest for 3 yrs as (39*3) = 117.

Next step, we subtract (815 - 117) to get Principal amt for a yr as Rs. 698.

Brief explanation for last step:

815 = Principal amt + int for 3 yrs ......equation 1.
117 = int for 3 yrs ......equation 2.

Now subtract both equations, we get the principal amount

I hope that this explanation will be helpful to you.

Hi Friends!
Principle = the amt u borrowed
Interest = the small additional amt u pay for the amt u
borrowed

First let me explain u d question
In the question,
A sum of money at simple interest amounts to Rs. 815 in 3 years means the Principle amt together wit the interest paid for 3 yrs is Rs. 815 and similarly Principle amt together wit the interest paid for 4 yrs is Rs. 854

Therefore, if we subtract (854-815) we get the simple interest for 1 year as Rs. 39

Then, we calculate simple interest for 3 yrs as (39*3)= 117

Next step, we subtract (815 - 117) to get Principle amt for a yr as Rs. 698

Brief explanation for last step:

815 = Principle amt + int for 3 yrs ......equation 1
117 = int for 3 yrs ......equation 2

now subtract both equations, we get the principle amt

I hope tat this explanation will be helpful to u

@All.

Principle = the amt u borrowed
Interest = the small additional amount you pay for the amount you borrowed

First, let me explain to you The question.

In the question,

A sum of money at simple interest amounts to Rs. 815 in 3 years means the Principle amt together wit the interest paid for 3 yrs is Rs. 815 and similarly Principle amt together wit the interest paid for 4 yrs is Rs. 854.

Therefore, if we subtract (854-815) we get the simple interest for 1 year as Rs. 39.
Then, we calculate simple interest for 3 yrs as (39*3)= 117.
Next step, we subtract (815 - 117) to get Principle amount for a yr as Rs. 698

Brief explanation for last step:

815 = Principle amt + int for 3 yrs ---> equation 1.
117 = int for 3 yrs ---> equation 2.

Now subtract both equations, we get the principle amount.

Hi, I cannot understand one thing that how could be the amount increasing every year is constant?

I mean if suppose 100 is the principle and rate is 10 percent then for the first year the amount will be 110, 2nd year it will be 121, 3rd year it will be 133.10.

Now 133.1 -121 is not equal to 121-110 also not equal to 110 -100 so the increasing amount is not constant. In this problem, how can we take the increasing amount constant and directly subtract it and divide it?

I mean how is it possible that the increasing amount remains 39 over three years?

I will explain in a simple way.

We have A = P + I.

815 = P + I -----> Eq 1.

854 = P + I -----> Eq 2.

Subtract Eq 1 and 2.

Simple interest I = 815 - P - 854 + P

= 39 for 1year.

Then take for 3 years or 4 years.

You will get the same answer.

For 3 years:

39 * 3 = 117.

Or For 4 years:

39 * 4 = 156.

Then use formula A = P + I.

For 3 years:

815 = P + 117,

P = 815 - 117,

= 698.

For 4 years:

854 = P + 156,

P = 854 - 155,

= 698.

Take for 3 or 4 years answer will be same. I think the explanation is very useful.

@Tanuja

Use Vikram's explanation as reference

In case you didn't understand still, just logically understand that the:

Resultant sum = Principal + (SI * No. of years).

In the case of your example which is 9 years SI is 657 and 5 years SI is 555 so:

P + 9SI = 657 -------------(1)
P + 5SI = 555 -------------(2)

Subtracting (1) with (2) you get:

4SI= 102,
SI = 102/4,
=> SI = 25.5.

Substituting SI in (1) equation you get:

P + 9 (25.5) = 657,
P = 657 - 9 (25.5),
=> P = 427.5.

Sum amounts to 815 in 3 years.

Sum amounts to 854 in 4 years.

Find sum?

Let the sum be Rs. x.

x = principal amounts in 3 years = Rs. 815.

x = principal amounts in 4 years = Rs. 854.

Principal amount in 1 year = 39 I.

Interest of 1 year = Rs. 39.

Interest of 3 year = 3x39= Rs. 117.

Principal = x.
Rate = ?
Time = 3 years.
For 3 years.

Interest = Rs. 117.
Amount = Rs. 815.
Time = 3 years.

Let rate = R%.
A = p+I.
P = A-I.

= R(815-117).

Rate 698 answer.

Let the sum is Rs. X and rate of interest is y%.

We know A = P + SI where SI = (P * R * T) /100 Therefore, A = P + (P * R * T) /100.

Case 1 : A = 815, P = x, T = 3 years, R = y%.
A = x + (x * y * 3) /100->1

Case 2 : A = 854, P = x, T = 4 years, R = y%.

A = x + (x * y * 4) /100 ->2

Subtracting equation (1) from equation (2), we get x * y = 3900.

Now by putting this value of x * y = 3900 in any one of above two equation, we'll get sum = x = 698 Answer.

Let p=x nd after 3year A1=815 nd4year A2=854... A( is total amount)=p+i we no P=(A*100)/(100+TR) .......p nd R is equal for both A1 nd A2 .
so P1 =p2-------(eq1) we have formula P1=(A1*100)/(100+T1R)--------(2)
And P2=(A2*100)/(100+T2R)---------(3)
put eq2 and eq3 on eq 1 and putting all value we go Rate (R)=5.58 value of R input on eq 2 or eq 3 we got the value of p.