56.
A person invested in all Rs. 2600 at 4%, 6% and 8% per annum simple interest. At the end of the year, he got the same interest in all three cases. The money invested at 4% is:
• A.
Rs. 200
• C.
Rs. 800
• B.
Rs. 600
• D.
Rs. 1200
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Explanation :

Let the parts be x, y and [2600 � (x + y)]. Then,

 x x 4 x 1 100
=
 y x 6 x 1 100
=
 [2600 - (x + y)] x 8 x 1 100

 y x
=
 4 6
=
 2 3
or y =
 2 3
x

So,
 x x 4 x 1 100
=
2600 -
 5 3
x    x 8
100

4x =
 (7800 - 5x) x 8 3

52x = (7800 x 8)

x =
 7800 x 8 52
= 1200

Money invested at 4% = Rs. 1200.

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57.
A sum of money lent at C.I. annually gives Rs. 250 and Rs. 300 as interest in the first and the 2nd year. Find the rate of interest.
• A.
10%
• C.
15%
• B.
20%
• D.
18%
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Explanation :

Interest for Rs. 250 for one year = Rs. 50

Interest for Rs. 100 for one year =

50 x 100  = 20%
250

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58.
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
• A.
Rs. 6400
• C.
Rs. 7200
• E.
None of these
• B.
Rs. 6500
• D.
Rs. 7500
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Explanation :

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 � x).

Then,
 x x 14 x 2 100
+
 (13900 - x) x 11 x 2 100
= 3508

28x - 22x = 350800 - (13900 x 22)

6x = 45000

x = 7500

So, sum invested in Scheme B = Rs. (13900 � 7500) = Rs. 6400.
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59.
A sum of Rs. 1550 was lent partly at 5% and partly at 8% p.a. simple interest. The total interest received after 3 years was Rs. 300. The ratio of the money lent at 5% to that lent at 8% is:
• A.
5 : 8
• C.
16 : 15
• B.
8 : 5
• D.
31 : 6
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Explanation :

Let the sum lent at 5% be Rs. x and that lent at 8% be Rs. (1550 � x). Then,

Then,
 x x 5 x 3 100
+
 (1550 - x) x 8 x 3 100
= 300

15x - 24x + (1550 x 24) = 30000

9x = 7200

x = 800

Required ratio = 800 : 750 = 16 : 15

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60.
David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?
• A.
Rs. 5000
• C.
Rs. 8000
• E.
None of these
• B.
Rs. 6500
• D.
Cannot be determined
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Explanation :

Let x, y and z be the amounts invested in schemes A, B and C respectively. Then,

 x x 10 x 1 100
+
 y x 12 x 1 100
+
 z x 15 x 1 100
= 3200

10x + 12y + 15z = 320000 ...(i)

Now, z = 240% of y =
 12 5
y ...(ii)

And, z = 150% of x =
 3 2
x x =
 2 3
z =
 2 3
x
 12 5
y =
 8 5
y ...(iii)

From (i), (ii) and (iii), we have :

16y + 12y + 36y = 320000

64y = 320000

y = 5000

Sum invested in Scheme B = Rs. 5000.

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