Aptitude - Simple Interest - Discussion

@All.

Here it includes the interest every six months for calculating the principal. So they are calculating 105.

@All.

Here is the clarification.

(i) When "T" i.e., the time is given in months then it should be divided by 12 to convert into years.

(ii) When "T" i.e., the time is given in days then it should be divided by 365 to convert into years.

I am not getting it.

How they are calculating 105. It should be 100, right?

Jadhav, it is written in the question he adds interest obtained, after every six months.. So interest obtained in 6 months was 5rs
He added this to principal after 6 months and calculated SI for the rest 6 of months using this added principal amount (using 105)..he now gets principal as 5.25
So, for first six months , SI=5
Remaining six months, SI=5.25
Total SI =10.25
Hope this helps

How can you add, the interest calculated for the first six months to the principal value to calculate interest for the last six months?

I thought in simple interest we consider only the principal amount and not the interest associated with it from the previous months.

Please clear this to me.

The question said at the interest rate of 10% which probably means for 1year per annum, but he includes every 6 months interest. That means an interest rate of 6 months will become (5% half of 1 year) + another 6 months (5%half of 1year).

Now, using the effective rate of interest formula.
i,e (a + b + a * b/100),
(5+5 + 5 * 5/100)
(10 + 25/100),
(10 + 0.25),
(10.25) answer.

Do effective rate of interest mean interest for 1 year?

Easy and clear explanation, Thanks @Saiteja.

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.

@Lakshmy answer.

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