Question

a)In how much time will simple interest on a sum of money be 2/5th of the sum, at the rate of 10% per annum  b) At what rate of interest will simple interest be half the principal in 5 years. c)A sum of money amounts to Rs. 1265 in 3 years and to Rs.1430 in 6 years, at simple interest. Find the sum and the rate percent.

Answer 1

Let the sum of money = A
$S.I = \frac{P*R*T}{100}$
P = Principal amount
R = Rate percent
T = Time
a).⇒A/Q,
          S.I of sum = 2/5 of sum
$or, \frac{ART}{100} = \frac{2}{5} A \\ or, \frac{A*10*T}{100} = \frac{2A}{5}$
$\frac{T}{10} = \frac{2A}{5A} \\ or,T = 20/5 = 4$
therefore time = 4 years

b).⇒A/Q,
               S.I = 1/2 of principal amount in five years
$or, \frac{PRT}{100} = \frac{1}{2} P \\ \frac{P*R*5}{100} = p/2 \\ or,R = 100/10 = 10$
therefore Rate = 10%per annum

c).⇒Sum of money (A) = (P+S) ,where P = principal amount   and S is S.I of three years
A/Q,
           Sum of money in 3 years($A_3$) = 1265
or   P+S = 1265  -------(1)
            Sum of money in 6 years ($A_6$) = (P+2S)
or,   P+2S = 1430  --------(2)
Now ,Equation (2)-(1) ,,
        S = 165 = S.I of three years
then P = 1100  = principal amount
now,
$S.I = \frac{PRT}{100}$
$165 = \frac{1100*R*3}{100} \\ or, R = \frac{165}{33} = 5$
therefore Rate = 5%

Answer 2

a) let the sum of be x
2x/5=x*10*t/100
⇒2=10t/20
⇒t=4 yrs


b)let the principal be x
  si=x/2
x/2=x*5*r/100
⇒50=5r
⇒r=10%

c) amt after 3 yrs=P+I=1265..........(i)
amt after 6 yrs=P+2I=1430............(ii)
subtracting (ii) frm (i)
we get I=165
 substituting in eqn (i)
we get,P+165=1165
⇒P=1100
165=1100*r*3/100
⇒r=5%