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Simple Interest

Theory and Formula



Questions

Q1. On a sum SI is
1/16
time of sum, and number of years are 4 times to rate of interest . find time.

Solution.
SI =
pnr/100
⇒
x/16
=
x . 4r . r/100


r2 =
100/64
⇒ r =
10/8
%

t = 4r = 4 x
10/8
= 5 years
Solution

Q2. Find the difference between SI and CI for two years on Rs.1500 at 15% p.a.

Solution.
Difference of SI & CI = P(
r/100
)2

= 1500(
15/100
)2

=
1500 x 225/100 x 100


=
3375/100
= 33.75
Solution

Q3. The SI and CI for two years on a certain sum is Rs.310 and Rs.340 respectively find the sum.

Solution.
2pr/100
=310 ⇒ pr = 15500

P(
r2/100
) = Difference of SI & CI ⇒ P(
r/100
)2 = 30

pr(r) = 3,00,000

15500(r) = 3,00,000 ⇒ r = 19.35%
Solution

Q4. A sum amounts to Rs.2240 in two years at SI, and amounts to Rs.2600 in five years , find principal .

(a) Rs.900 (b) Rs.1500 (c) Rs.2000 (d) Rs.1800

Solution.
(c) Rs.2000
Solution

Q5. Rs. 3500 is distributed in two part and both part gains same interest for two years. Rate of interest are 8% and 6% respectively . find the ratio of value(distributed) .

Solution.
Value will be distributed in the ratio of

1/r1t1
:
1/r2t2


1/8 x 2
:
1/6 x 2
⇒
1/16
:
1/12
⇒ 3 : 4
Solution

Q6. A sum of money becomes triple in 20 years . find the rate of SI .

Solution.
SI =
pxr/100
⇒ 2p =
p . 20 . r/100
⇒ r = 10 %
Solution

Q7. A money at the rate of 14% per annum , in how many years it will be 8 times ?

(a) 80 years (b) 50 years (c) 60 years (d) 20 years

Solution.
(b) 50 years

[(n - 1) x 100]/r

= (7 x 100)/14

= 100/2 = 50
Solution

Q8. Find the rate of SI, if SI of 10 years is
2/ 5
of amount .

Solution.
Let A = Rs. x

SI =
2/ 5
x

P =
3x/ 5


SI =
prt/ 100
⇒
2/ 5
x =
3x . r . 10/ 500


r = 6.66%
Solution

Q9. In how many years a money becomes 7 time at the rate of 12% p.a. SI .

Solution.
t =
(n - 1) x 100/r


(7 - 1) x 100/ 12
=
6 x 100/ 12
= 50 yrs

or

6p =
p x 12 x t/ 100
⇒
600/ 12
= t ⇒ t = 50 years .
Solution

Q10. Rs . 3689 is divided into three parts such that their interest after 1,2,and 3 years may be equal. The rate of interest is 5% . find the ratio between these part .

Solution.
1/ r1 t1
:
1/ r2 t2
:
1/ r3 t3
(Trick)

1/ 5
:
1/ 10
:
1/ 15
= 3 : 2 : 1
Solution