Aptitude - Simple Interest - Discussion

I am not getting this.

Please, anyone, explain me in detail to get it.

How come 100 * 2 here? explain.

Please explain clearly.

@Susmita.

Why we take principal 100 for 1 year it is 105 when we calculate the rate in the last?

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs. 100 x 10 x 1 = Rs. 5.
100 x 2.
S.I. for last 6 months = Rs. 105 x 10 x 1= Rs. 5.25 // How 105?
100 x 2.
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25.

Effective rate = (110.25 - 100) = 10.25%.

It is simple and not compound interest, so effective interest rate should be 10% only.

The effective interest rate should be 10% only and not 10. 25% since it is simple and not compound interest! Correct me If I am wrong.

The principal should be 100. It's simple interest not compound interest that interest will be calculated on total amount.

@Lakshmy answer.

Why should we divide total S.I by 100/x, can you help me out for this?

Let the principal amount be x.
i.e p=x and rate of interest r=10.
and time = 1/2 (half year).

For first six months simple interest i = ptr/100.
=> i =((x )(1/2)(10))/100,

By solving above equation we get i= x/20,
Now new principal amount =x+(x/20) =>21x/20,
=>p=21x/20.

For second six months simple interest i= ptr/100.
=> i=( (21x/20)(10)(1/2) )/100.
=>i=21x/400.

Now total amount TA is = principal amount +interest on first six months +interest second six months.
=>TA=(x)+(x/20)+(21x/400).
=>TA=441x/400,

Now interest for 1 year is= total amount TA -actual principal amount.
ie. i= (441x/400)-x.
i= 41x/400.
Now for an effective rate of interest r.
i=ptr/100.
p=x,r=?,t=1(for complete 1 year),i=41x/400(interest for complete one year).
=> 41x/400=( (x)(1)(r) )/100.
=> r=41/4.
=> r=10.25.