Aptitude - Simple Interest - Discussion

Total amount after 1 year 110.25. Principal is 100 So SI = 10.25.

SI = PxRxT/100.

10.25 = 100 x R x 1/100.

R = 10.25.

In the solution they directly its written as effective rate.

Here is a shortcut for you.

Interest is 10% percent that means per year 10 rs will increase. If you take 100 as principal that means interest would be 5 Rs for 6 months. Now the total principal becomes 105 now again 5% interest for 6 months becomes 5.25. Now total interest is 5+5.25 = 10.25.

Otherwise x+y+(xy/100) = 5+5+(25/100) = 10.25.

Say X is the Principal amount
then SI for first the 6 months= X*10/100*1/2 =X/20

SI for the next 6 months =21X/20*10/100*1/2= 21X/400
[Here Principal amount is taken as X+ X/20= 21X/20]

SI for one year =X/20+ 21X/400 = 41X/400

Now With Principal amount X and SI 41X/400 for one year we have to find the rate of interest, say y
y= 100*41X/400*1/X = 10.25//

Rate of interest in already given as 10%. Then what is effective rate of interest.

As amount is not given so we will have to consider the amount to be 100
hence let P=100.

Now the lender add interest after every six month so we will have to calculate SI for every six month add then add this SI toh the P.

Hence
SI=P*R*T/100
=100*10*1/100*2(6 monh=1/2 year)
=5

Now P becomes
P=100+5
=105, this is SI for 1st 6 month
Now calculate SI for last 6 motnh
SI=105*10*1/100*2
=5.25
P=5+5.25+100
=110.25, this is the amount at the end of 1 year.

Now SI for I year=110.25-100
=10.25
Now we have to calculate rate
SI=P*R*T/100
10.25 =100*R*1/100
R=10.25 //

SI for 1 year =10.25
10.25=100*R*1/100
=10.25
Hence r=10.25

Hows it possible to solve without time?

How did they got 105?

S.I is always calculate on original sum. But here the last six month S.I is calculate on Amount at the end of 1st 6 month. Is'nt this is the concept of C.I not of S.I ?

How did they got 105 and why are they multiplying it 2?

Please explain me.