Aptitude - Simple Interest - Discussion

Is 698 is principal amount?

Why should we apply like this;

s.i for 1 year = Rs 854-815=39
1yr = 39 then 4y = 156
then 854-156=698.

@Divya.

Its a initial amount.

Thanks for explaining.

Basic formula of to find r% and p%.

When give two amounts and two years to find p formula,
(A1*T2-A2*T1)/T2-T1.

R% FORMULA.
(A2-A1)/(A1*T2-A2*T1).

Can't this question be solved using formula
p=100*si/r*t.

Total amt = p+si.
815 = p+si.
si = 815-p.
854 = p+si.
si = 854-p.
Substituting in formula,
p = 100*815-si/r*3.

Can anyone please help how to solve using this method of substitution.

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.

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.

You can use the formula, SI= PRT.

Here, R= (854-815)/815= 0.0475, T= 3 years, & P= 815.
Therefore, SI= 815*0.0475*3= 117.
Final answer= 815-117= 698.

You can replace T= 4 years & P= 854, the answer is same.

What is the percentage of the interest?