Pareekshavijayi e-Book

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14 Veto
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6. A certain sum of money doubles
itself in 5 years. In how many
years will it become 8 times at the
same rate of compound interest?
(a) 15 years
(c) 5 years
Ans: (a) 15 years
(b) 10 years
(d) 3 years
Short-cut
If a sum becomes x times in y
years at CI then it will be x (n)
times in ny years
Solution:
2 times in 5 years
8 times 2 (3) in 3 x 5 = 15 years
7. A sum of money tribles in 4 years.
In how many years will it amount
to 9 times at the same rate of
compound interest?
(a) 2 years
(c) 8 years
Ans: (c) 8 years
Solution:
3 times in 4 years
(b) 4 years
(d) 12 years
9 times 3 (2) in 4 x 2 = 8 years
8. At what rate percent compound
interest does a sum of money
become nine-fold in 2 years?
(a) 50% (b) 100%
(c) 15% (d) 200%
Ans: (d) 200%
Short-cut
If a certain sum becomes ‘m’
times in ‘t’ years, the rate of
compound interest ‘r’ is equal
to 100 ⎡( ) 1 t
m −1⎤
⎣ ⎦
Solution:
Rate % = ( ) 1 2
100 ⎡ 9 −1⎤
⎣ ⎦
= 100[3-1] = 100 x 2 = 200%
9. At what rate percentage
(compound interest) will a sum
of money become 8 times in 3
years?
(a) 100% (b) 200%
(c) 50% (d) 150%
Ans: (a) 100%
Solution:
Rate % = ( ) 1 3
100 ⎡ 8 −1⎤
⎣ ⎦
= 100[2-1] = 100%
10. Find the difference between the
compound interest and the simple
interest for the sum of Rs.1500 at
10% per annum for 2 years?
(a) 1000 (b) 100
(c) 50 (d) 15
Ans: (d) 15
Short-cut
The difference between SI and CI
on a certain sum of money for 2
2
years is PR
2
100
Solution:
P=1500 R = 10%
2
PR 1500× 10×
10
= =
2
15
100 100×
100
11. The difference between the simple
and the compound interest on a
certain sum of money for 2 years
at 4% per annum is Rs.1. Find the
sum?
(a) 625 (b) 125
(c) 525 (d) None of these
Ans: (a) 625
Solution:
2
PR
= 1
2
100
P× 4×
4
= 1
100×
100
100×
100
P = = 625
4×
4
12. Find the difference between CI and
SI on Rs.8000 for 3 years at 2.5%
per annum?
(a) 12.31 (b) 10.25
(c) 15.125 (d) 20.38
Ans: (c) 15.125
Short-cut
Difference between CI and SI for
2
3 year is PR ⎡ R ⎤
3
2
100 ⎢
+
⎣ 100⎥
⎦
Solution:
Here P = 8000
R = 2.5%
Difference between SI and CI
2
PR ⎡ R ⎤
= 3
2
100 ⎢
+
⎣ 100⎥
⎦
8000× 2.5× 2.5 ⎡ 2.5 ⎤
= 3+
100× 100 ⎢
⎣ 100⎥
⎦
8000× 2.5× 2.5×
302.5
=
100× 100×
100
8× 25× 25×
3025
=
100× 100×
100
121
=
8
= 15.125
13. A certain sum of money invested at
compound interest, compounded
annually, becomes Rs.8820 in 2
years and Rs.9261 in 3 years. Find
the rate of interest and the sum?
(a) 5%, 4000 (b) 5%, 8000
(c) 10%, 4000 (d) 10%, 8000
Ans: (b) 5%, 8000
Short-cut
A certain sum of money
invested at compound interest,
compounded yearly, becomes
A1 in n years and Rs.A2 in (n+1)
years then
100
Rate % =
⎛ A ⎞
1
P = A1
⎜ ⎟
⎝ A
2 ⎠
Solution:
n
( A − A )
A
2 1
1
%
( )
100 9261 8820
Rate% =
P =
−
8820
×
8820
n
⎛ A ⎞
1
A1
⎜ ⎟
⎝ A
2 ⎠
2
100 441
= = 5%
⎛8820
⎞
= 8820⎜ ⎟
⎝ 9261 ⎠
2
⎛20
⎞
= 8820× ⎜ ⎟
⎝ 21 ⎠
= 8000
POINTS TO REMEMBER
1. Average of first ‘n’ natural numbers
⎛n+
1⎞
= ⎜ ⎟
⎝ 2 ⎠
2. Average of first ‘n’ even numbers = n+1
3. Average of first ‘n’ odd numbers = n
4. Average of cons-ecutive numbers
Revision
Laws of exponents
a xa = a
m n m+n
m
a
n
a
= a
m n
(a ) = a
1
m-n
mn
-n
a = a
n
0
a = 1
(ab) = a xb
⎛a⎞
⎜ ⎟
⎝b⎠
⎛1
⎞
⎜ ⎟
⎝a
⎠
n n n
n
-m
=
NOTE
a
b
n
n
= a
m
POWERS OF 10
10 0 = One
10 1 = Ten
10 2 = Hundred
10 3 = Thousand
10 4 = Myriad
10 6 = Million
10 9 = Billion
10 12 = Trillion
10 15 = Quadrillion
10 18 = Quintillion
10 21 = Sextillion
First No. + Last No.
=
2