An amount of Rs. 1,00,000 is invested in two types of shares. The first yields an interest of 9% per annum and the second, 11% per annum. If the total interest at the end of one year is 9 3/4 %, then the amount invested in each share was:
A.  Rs 52,500 ; Rs 47,500  
B.  Rs 72,500 ; Rs 27,500  
C.  Rs 62,500 ; Rs 37,500  
D.  Rs 82,500 ; Rs 17,500  
E.  None of these 

Let the sum invested at 9% be Rs. a and that invested at 11% be Rs. (100000  a).
Then,
a x 9 x 1
100
+
(100000  a) x 11 x 1
100
=
100000x
39
x
1
4
100
9a + 1100000  11a
=
39000
= 9750
100
4
2a = (1100000  975000) = 125000
a = 62500.
Sum invested ar 9% = Rs. 62500.
Sum invested ar 11% = Rs. (100000  62500) = Rs. 37500.
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Divide Rs. 2379 into 3 parts so that their amount after 2,3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is:
 759
 818
 792
 828
 None of these

Let the parts be a, b and [2379  (a + b)].
a +
(a x 2 x
5
)= b +
(b x 3 x
5
)= c +
(c x 4 x
5
)
100
100
100
11a
=
23b
=
6c
= K
=>
a =
10K
, b =
20K
, c =
5K
10
20
5
11
23
6
But a + b + c = 2379
10K
+
20K
=
5k
= 2379
1380K + 1320K + 1265K = 2379 x 11 x 23 x 6
11
23
6
K =
2379 x 11 x 23 x 6
=
3 x 11 x 23 x 6
3965
5
a =
10
x
3 x 11 x 23 x 6
= 828.
11
5
Hence, the first part is Rs. 828.
How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% pa simple interest?
 21
 28
 56
 76
 None of these

Simple interest is given by the formula SI = (P x T x R)/100,
where P is the principal,T is the number of years for which it is invested,
R is the rate of interest per annum. In this case,
Rs. 1250 has become Rs.10,000.
Therefore, the interest earned = 10,000 – 1250 = 8750.
8750 = [(1250 x T x 12.5)/100]
T = 700 / 12.5 = 56 years
A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks?
 100
 80
 70
 60
 None of these

Let the maximum marks be x.
From the given statement pass percentage is 42%  12% = 30%
By hypothesis, 30% of x – 20% of x = 10 (marks)
i.e., 10% of x = 10
Therefore, x = 100 marks.
A sum of Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3%, it would amount to how much?
 764
 992
 850
 770
 None of these

S.I = Rs. (920 – 800) = Rs. 120; P = Rs. 800, T = 3 yrs
R = ( 100 X 120 )% = 5%
800 X 3
New rate = (5 + 3) % = 8%
New S.I. = Rs. (800 X 8 X 3) == Rs. 192.
100
New amount = Rs. (800 + 192) = Rs. 992