Question :

What is the sum which earned interest ?

Statements :

a. The total simple interest was Rs. 9000 after 9 years.
b. The total of sum and simple interest was double of the sum after 6 years.

I= PTR100

At 5% more rate, the increase in S.I for 10 years = Rs.600  (given)

So, at 5% more rate, the increase in SI for 1 year = 600/10 = Rs.60/-

i.e. Rs.60 is 5% of the invested sum

So, 1% of the invested sum = 60/5

Therefore, the invested sum = 60 × 100/5 = Rs.1200

let the sum lent at 5% be Rs.x and that lent at 8% be Rs.(1550-x). then, 

Interest on x at 5% for 3 years + interest on (1550-x) at 8% for 3 years = 300

 x*5*3100+1500-x*8*3100=300 

 x=800

Required ratio =  x : (1550-x) = 800 : (1550-800) = 800 : 750 = 16 : 15

Clearly, any of the three will give us the answer

We know that, R = (100 x S.I) / (P x T)

Now I gives, S.I = Rs. 4000.

        II gives,  T = 4 years.

But, P is unknown. So, we cannot find R.

So, given data is insufficient to get R.

Let the rate be R% p.a.

I  gives, P = Rs. 8000 and T = 4 years.

II gives, S.I = Rs. (8800 - 8000) = Rs. 800.

R = [100 x S.I] / [p x t ]= (100 x 800)/(8000 x 4) = 2 ½ % p.a

Thus, I and II both are needed to get the answer.

Simple interest is given by the formula SI = (pnr/100), where p is the principal, n is the numberof years for which it is invested, r is the rate of interest per annum

In this case, Rs. 1250 has become Rs.10,000.

Therefore, the interest earned = 10,000 – 1250 = 8750.

8750 = [(1250 x n x 12.5)/100]

=> n = 700 / 12.5 = 56 years.

From the information provided we know that,

Principal + 8% p.a. interest on principal for n years = 180 …….. (1)

Principal + 4% p.a. interest on principal for n years = 120 ……… (2)

Subtracting equation (2) from equation (1), we get

4% p.a. interest on principal for n years = Rs.60.

Now, we can substitute this value in equation (2),

i.e Principal + 60 = 120

= Principal = Rs.60.

We know that SI = , where p is the principal, n the number of years and r the rate percent of  interest.

In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.

Therefore, 60 =(60*n*4)/100

=> n = 100/4 = 25 years.