31.
If in a certain number of years Rs. 3000 amount to Rs. 4320 at compound interest, in half that time Rs. 3000 will amount to:
• A.
Rs. 3400
• C.
Rs. 3800
• B.
Rs. 3600
• D.
Rs. 3520
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Explanation :

 Let r% be the rate and n years be the time.

 Then, 4320 = 3000 1 + r n 100

1 + r   n = 4320  = 1.44
100 3000

1 + r   n/2 =
 1.44
= 1.2
100

In n  years, Rs. 3000 will amount to
2

 3000 1+ r n/2 = 3000 x 1.2 100

 = Rs. 3600.

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32.
A sum of Rs. 12,000 deposited at compound interest becomes double after 5 years. After 20 years, it will become:
• A.
Rs. 96,000
• C.
Rs. 1,24,000
• B.
Rs. 1,20,000
• D.
Rs. 1,92,000
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Explanation :

12000 x   1 + R   5  = 24000
100

1 + R   5 = 2
100

 1 + R 5 100
4  = 24 = 16

 1 + R 20 100
= 16

P
 1 + R 20 100
= 16P

12000   1 + R   20  = 16 x 12000 = 192000
100

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33.
A sum is invested at compounded interest payable annually. The interest in two successive years was Rs. 500 and Rs. 540. The sum is
• A.
Rs. 3750
• C.
Rs. 5600
• B.
Rs. 5000
• D.
Rs. 6250
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Explanation :

S.I. on Rs. 500 for 1 year = 540 - 500

 = Rs. 40

Rate = 100 x 40  = 8%
500 x 1

 and Sum = Rs. 100 x 500 8 x 1

 = Rs. 6250

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34.
Sanjay borrowed a certain sum from Anil at a certain rate of simple interest for 2 years. He lent this sum to Ram at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 4200 as compound interest but paid Rs. 4000 only as simple interest. Find the rate of interest.
• A.
15%
• C.
35%
• B.
20%
• D.
10%
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Explanation :

 Suppose the sum borrowed = Rs x

 Rate of interest = R%

 Time = 2 years

4000 = x x R x 2 Rx = 200000 ..(i)
100

 Now

x   1 + R   2 = x + 4200 xR2 + 2Rx  = 4200
100 10000 100

 20R + 4000 = 4200

 R = 10.

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35.
If a sum on compound interest becomes three times in 4 years, then with the same interest rate, the sum will become 27 times in:
• A.
8 Years
• C.
24 Years
• B.
12 Years
• D.
36 Years
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Explanation :

P   1 + R   4 = 3P     1 + R   4  = 3 ...(i)
100 100

Let P
 1 + R n 100
= 27P
 1 + R n 100
= 27 = (3)=
 1 + R 4 100
3   [using (i)]

 1 + R n 100
=
 1 + R 12 100
n = 12

Required time = 12 years.

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