13.Mallapragada's Mathematics (Simple Interest-1)

IMPORTANT FACTS AND FORMULAE

1. Principal: The money borrowed or lent out for a certain 

                       period is called the Principal or the sum.

2. Interest: Extra money paid for using other's  money is called 
                    interest.

3. Simple Interest (S.I): If the interest on a sum borrowed for a 
     certain period is reckoned uniformly,  then                                 

     it is called Simple interest.

 Let Principle =p, Rate = R% per annum (p.a) and Time = T years Then 

(i) S.I = [P X R X T] / 100

(ii) P = {100 x S.I} / {R x T}
     R = {100 x S.I} / {P x T}
     T = {100 x S.I} / {P x R}    

                                                                          

1. At the rate of 61/2% p.a simple interest, a sum of the Rs. 4800 will earn how much interest in 2 ears 3 months.
(a)    Rs. 956   (b)   Rs.815      (c)    702   (d) 1000

2. The simple interest at x% for x ears will be Rs. x on a sum of:
(a)       100/x²        (b)  100/x     (c)   100x      (d)  x

3. What will be the simple interest earned on an amount of rS. 2000 in 9 months at the rate of 6 ¼% p.a.?

(a)  93.75                (b)  860                      (c)  1000         (d)  2000

4 The simple interest on Rs. 1820 from March 9, 2014 to May 2014 at rate 8% rate will be

(a) 9.12          (b)     22.50         (c) 29.00      (d)     30

5. A sum off etched a total simple interest of Rs. 4016.25  at the rate of 9 p.c. p.a  in 5 ears What is the sum?

 (a)    8925              (b)  860                      (c)  1000         (d)  2000

6. Find The simple interest on the Rs 3000 at 6 ¼% per annam for the period from 4^th feb. 2014 to 18 april 2014.

(a)      37.25            (b)  860                      (c)  1000         (d)  2000

7. Find the interest on Rs. 50,000 at 16 2/3 % p.a. for 9 months

(a)   2083.33               (b)  860                      (c)  1000         (d)  2000

8. A sum of the simple interest at 13 1/2 % .p.a amounts to Rs. 2502.50after 5 ears find the sum.

(a)      1494.02            (b)  860                      (c)  1000         (d)  2000

9. What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?

(a)     112             (b)        12      (c) 122          (d) 120

10. a sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 4 months.  The rate of interest?

(a)    27%             (b)  6 ½%                 (c) 6 ¾%          (d)  6 ¼ %

11A sum of Rs. 12,000 amounts to Rs. 15000 in 4 years at the rate of simple interest. What is the rate of interest?

(a)      5.55         (b)      5%           (c)   6%        (d)  6.25%

12. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?

(a)  4 years           (b)   3 years              (c)   5 years        (d) 

13. A sum of money amount to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple  interest .  The rate of interest per annum is:

(a)  15 %           (b)  5%              (c)  8 %        (d)  12%

14. The simple interest on Rs. 10 for 4 months at the rate of 3 paise  per  rupes per month is:

(a)  3.6           (b)  2.40              (c)  1.20        (d)  1.60

15. A sum of money at simple interest amounts to Rs. 1000 in 3 ears and rs. 1200 in 4 years. The sum is:

(a)   300         (b) 400              (c)    350     (d)450

16. A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs. 1000 after a further period of 5 years.  The sum is

(a)  600          (b)    650           (c) 700        (d) 750

17. What will be the ration of simple interest e arned by certain amount at the sane rate if interest for 6 years  and that for 9 years.

(a)  3:2          (b) 2:3              (c) 5:3        (d) 3:5

18. In how maney  years Rs.150 will produce the same interest @ 8% as Rs. 800 produce in 3 years @ 4 ½%

(a)    5years        (b)       9Years        (c)   8Years    (d) 6 Years

19. The simple interest on a sum of money  will be Rs. 600 after  10 years.  If the principal is trebled after 5 years what will be the total interest at the end of the tenth year

(a)1200            (b)  1000       (c) 600      (d)1100

20. at what rate percent per annum will a sum of money double is 16 years?

(a)6.25  (b) 6.00     (c)   5.25    (d)7.25

                                                           

1. At the rate of 61/2% p.a simple interest, a sum of the Rs. 4800 will earn how much interest in 2 years 3 months.
Ans. P.= 4800 R. 6 ½% = 13/2  T.= 2 3/12 = 2 ¼ = 9/4 years
         I = PTr/100 = 4800 x 13/2 x 9/4 x 1/100 = Rs. 702
          
2. The simple interest at x% for x ears will be Rs. x on a sum of:
Ans. S.I. = x, t= x    R = x    P= ?      I = PTR/100  x = P x x/100  

          P = 100  x/ x x  =  Rs. 100/x

3. What will be the simple interest earned on an amount of rS. 2000 in 9 months at the rate of 6 ¼% p.a.?

Ans.  P = 2000    R = 6 ¼ = 25/4       T = 9/12 = ¾

          I= PTR/100  = 2000 x ¾ x 25/4 x 1/100 =  Rs. 93.75

4 The simple interest on Rs. 1820 from March 9, 2014 to May 2014 at rate 8% rate will be

Ans. P = 1820   Time 9-3-2014 to May 2014 = (22 + 30 + 31) = 73 days

        One year = 365 days = 73/365   R = 8 %

        I= PTR/100   = 1820 x 73/365 x8 x 1/100 = Rs. 29.12

5. A sum off etched a total simple interest of Rs. 4016.25  at the rate of 9 p.c. p.a  in 5years What is the sum?

Ans. P = ?   S.I. = 4016.25    9 %   T = 5    I = PTR/100  = P = 100 x I/TR

         100 x 4016.25 /5 x 9 = 20 x 4016.25/9 = 80325/9=Rs. 8925

6. Find The simple interest on the Rs 3000 at 6 ¼% per annam for the period from 4^th feb. 2014 to 18 april 2014.

Ans. P = 3000  R= 6 ¼ % = 25/4%  T =4^th feb. 2014 to 18 april 2014.

         T = (24 + 31 + 18) days  = 73/365 =1/5 years

         I = 3000 x 1/5 x 25/4 x 1/100 = 30 x 5/4 = 150/4 =37.5

7. Find the interest on Rs. 50,000 at 16 2/3 % p.a. for 9 months

Ans. P = 50,000      R = 50/3   T = 9/12 = ¾

        I = 50,000 x 50/3 x ¼ x 1/00 = 25000/12 = Rs. 2083.33

8. A sum of the simple interest at 13 1/2 % .p.a amounts to Rs. 2502.50 after 5 years find the sum.

Ans..  Let P.= x,   A. 2502.50,    R= 13 ½% = 27/2 %  T= 5

          I = x x 5 x 27/2 x 1/100 = 27x/40

          A= p + I = x + 27x/40 = 67x/40

          2502.50 = 67x/40    Therefore 67 x = 40 x 2502.50

         X = 1494.02

9. What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?

Ans.  Let P = x , T = 2 R= 5   S.I. = A –P = 132-x

         I=PTR/100 =,  132-x = (x .2. 5)/100

        10 x = 13200 – 100x

        110 x = 13200 ,     x = 13200/110 = Rs. 120

10. a sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 years and 4 months.  The rate of interest?

Ans. P = 1600    S.I. = 252  T = 2 4/12Years = 2 1/3 = 7/3  r = 100 x I/PT

        100 x 252 / 1600 x 7/3 = 100 x 252 x 3 /1600 x 7 = 75600/11200

        R = 6.75 % = 6 3/4% = 27/4 %

11A sum of Rs. 12,000 amounts to Rs. 15000 in 4 years at the rate of simple interest. What is the rate of interest?

Ans. P = 12,000   A.=  15000  I = A-P = 3000  R = ?   T = 4

        R = 100 x I/pt,   = (100 X 3000)/ (12000 X 4 )= 300000/48000 =  

        Therefore R =  6.25%    

12. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?

Ans. P = Rs. 450,   I= 81  R = 4.5% T = ?

         T = 100 x I /PR  = 100 x 81/ 450 x 4.5,

         8100/2025 = 4 Years          

13. A sum of money amount to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple  interest .  The rate of interest per annum is:

Ans. S.I for three years = 12005 – 9800 = R. 2205

         S.I = 2205/3,  S.I for 5 years = 2205/3 x 5  =(2205 x 5)/3 =3675

          Principle = A –I = 9800 – 3675 = R. 6125

          R = 100 x I/P.T,   (100 x 3675)/ 6125 x 5  =12%

  

14. The simple interest on Rs. 10 for 4 months at the rate of 3 paise  per  rupes per month is:

  S.I. = 10 x 3 x 4/12 x 1/100 = 120/1200 = 0.1

15. A sum of money at simple interest amounts to Rs. 1000 in 3 years and Rs. 1200 in 4 years. The sum is:

Ans. S.I. for 1 year = A-P = 1200 -1000 =200

         S.I. for 3 years = 200 x 3=600

          P = A-I = 1000-600 =Rs.  400

16. A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs. 1000 after a further period of 5 years.  The sum is

S.I. = for 5 year = 1000-720=280

       2 years = 300/5 x 2 = Rs. 120

      P =- A-I = 720 – 120 = 600

17. What will be the ration of simple interest earned by certain amount at the sane rate if interest for 6 years  and that for 9 years.

Ans. Let the Principle = P rate R  Time = 6: 9

         Required Ratio = (Px Rx 6/100)/( PxRx9/100) = 6PR/9Pr=6/9=2/3

         Ratio 2:3

18. In how many years Rs.150 will produce the same interest @ 8% as Rs. 800 produce in 3 years @ 4 ½%

Ans. P = 800,  R. 4 ½%, T = 3  = I = 800x 3x 9/200 =Rs. 108

         P = 150    R = 8%  I =108     

         T = 100 x I/pxR = 100 x 108 / 150 x 8 =  10800/1200 = 9 Years.

19. The simple interest on a sum of money  will be Rs. 600 after  10 years.  If the principal is trebled after 5 years what will be the total interest at the end of the tenth year

Ans.  Let P = x , I = 600 t=10  

          R = 100 x I/PT  = 100 x 600/x 10  = 60000/10x   = 6000/x

,        S.I. of 1^st 5 years = x x 5x 6000/x x 1/100 = 300

      S.I Last 5 years = 3x 5 6000/x 100 = Rs. 900

      Toal Amount 900 + 300 =RS. 1200

20. at what rate percent per annum will a sum of money double is 16 years?

Ans. Let Principle = P     Time = 16  s.I = P

         R = 100 x P/ p x 16  = 100/16  = 6.25% = 61/4%