## Monday, 8 June 2015

1. The height of a tree increase every year 1/8 times .If the present height of the tree is 64 cm, then
what will be its height after 2 years?
(a) 76 cm (b) 80 cm (c) 81 cm  (d) 84 cm (e) None of these
Solution: (c) .
Initial height = 64
First year = 1/8(64) = 8
So 8+64 = 72cm
Second year = 1/8(72) = 9
So 9+72 = 81cm

2. The Simple Interest on a certain sum for 2 years is Rs.120 and the compound interest is Rs. 129. Find  the rate of interest
(a ) 14% (b) 15 % (c ) 12 % (d ) 12 % (e ) Cannot be determined
Solution ; (b).
Interest for first year in Simple Interest and Compound Interest are same
So we need to blind first year interest.
Simple interest for every year will be same
= Simple Interest for 2 years = 120
1 year = 120/2 = 60
So first year interest of Compound Interest = 60
The difference between simple interest and compound interest for 2nd year is ‘a’. So find a is what % of  60
= 9/60 X 100 = 15%

3. At what percentage annual compound interest rate, a certain sum amounts to its 27 times in 3 Years?
( a) 100%   (b ) 150 %   (c ) 75%   (d ) 200%   (e) 900%
Solution: (d).
Let the principal be P
N=3
Amount = 27P
= 27P = P ( 1+ R/100)3
While solving
(3)3 = ( 1+R/100)3
Therefore 3 = 1 + R/100
=R/100 = 3-1
So R = 200%

4. Find the least number of complete years in which a sum of money put out at 40% compound interest
will be more than double.
(a) 3yr   (b) 4 yr   (c) 5yr   (d) 8 yr   (e) None of these
Solution: (a).
Let the principal be ‘P’
Then P(1+40/100)n > 2P
While solving the above relation , we get
(140/100)n >2 => (7/5)n >2
= (1.4)n > 2
So n = 3
By trail sub the values for n
When n = 3
We get (1.4)3 is >2
Therefore number of years is 3

5. What amount will be received on a sum of Rs.15000 in 1 yrs at 10% per annum, if interest is
compounded half yearly?
(a) 4996.5 (b) 19996.5 (c) 23999.5 (d) 21609.25 (e) None of these
Solution: (5).
P = 15000
N = 1 ½ years N = 3/2
R = 10%, p.a. (for ½ year = 5%)
Since the interest is compounded
½ yearly the formula will be
Amount = P (1+ R/100)2N
= 15000 ( 1 + 5/100) 2 3/2
= 15000 ( 105/100)3
= 15000 x 21/20 x 21/20 x 21/20
= 138915/8
= 17364.375