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Compound Interest

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Question
SSCCGLENQA12042681
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A man borrows money at 3% per annum interest payable yearly and lend it immediately at 5% interest (compound) payable half-yearly and thereby gains ₹ 330 at the end of the year. The sum borrowed is

  • ₹ 17000

  • ₹ 16500

  • ₹ 15000

  • ₹ 16000

Solution

D.

₹ 16000

Shortcut Method:
Go with option, say 'option (d)' sum borrowed ₹16000
If principal  = ₹16000
Case I, When given on 3% interest p.a. then interest would be 3% on 16000 = ₹480
Case II, When given on 5% interest (compound) payable half-yearly then interest would be16000 space rightwards arrow with open parentheses 5 over 2 space equals space 2.5 percent sign space equals space 400 close parentheses on top left parenthesis 16000 plus 400 right parenthesis space equals space 16400 space rightwards arrow with left parenthesis 2.5 percent sign space equals space 410 right parenthesis on top
Total interest  = (400 + 410) = ₹ 810
Difference of interest = ₹ (810 - 480) = ₹ 330

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Question
SSCCGLENQA12043262
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A man invested a sum of money at compound interest. It amounted to Rs. 2420 in 2 years and to Rs. 2662 in 3 years. Find the sum.

  • Rs. 1000

  • Rs. 2000

  • Rs. 5082

  • Rs. 3000

Solution

B.

Rs. 2000

Rate of interest:
equals space open parentheses fraction numerator 2662 space minus space 2420 over denominator 2420 end fraction space cross times space 100 close parentheses space equals space 10 percent sign
Now,
 rightwards double arrow space space space space 2420 space equals space straight P open parentheses 1 plus straight r over 100 close parentheses squared rightwards double arrow space space space space 2420 space equals space straight P open parentheses 1 plus 10 over 100 close parentheses squared rightwards double arrow space space space space 2420 space equals space straight P space cross times space open parentheses 11 over 10 close parentheses squared
  rightwards double arrow space space 2420 space equals space straight P space cross times space 121 over 100 rightwards double arrow space space space straight P space equals space fraction numerator 2420 space cross times space 100 over denominator 121 end fraction space equals space Rs. space 2000

Question
SSCCGLENQA12042686
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A man spends ₹ 1800 monthly on an average for the first four months and ₹ 2000 monthly for the next eight months and saves ₹ 5600 a year. His average monthly income is

  • ₹ 2000

  • ₹ 2200

  • ₹ 2400

  • ₹ 2600

Solution

C.

₹ 2400

Total Spendings of man in a year
 = Rs. (4 x 1800 + 8 x 2000)
 = Rs. (7200 + 16000)
 = Rs. 23200
Savings = ₹ 5600 a year.
Total annual income  = (23200 + 5600) = ₹ 28800
∴ Average monthly income = 28800 over 12 space equals space Rs. space 2400

Question
SSCCGLENQA12042052
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A sum amounts to Rs. 2,916 in 2 years and to Rs. 3,149.28 in 3 years at same rate of compound interest. The sum is

  • Rs. 2500

  • Rs. 2400

  • Rs. 2250

  • Rs. 2000

Solution

A.

Rs. 2500

Interest  = 3,149.28 - 2,916 = 233.28
 Rate percent sign space equals space fraction numerator 233.28 over denominator 2916 end fraction space cross times space 100 space equals space 8 percent sign
Now,
2916 space equals space straight P open parentheses 1 plus 8 over 100 close parentheses squared 2916 space equals space straight P open parentheses 27 over 25 close parentheses squared
rightwards double arrow space space straight P space equals space fraction numerator 2916 space cross times space 25 space cross times space 25 over denominator 27 space cross times space 27 end fraction rightwards double arrow space space straight P equals space space Rs. space 2500

Question
SSCCGLENQA12042976
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A sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself?

  • 9

  • 27

  • 6

  • 3

Solution

C.

6

'X' becomes '3X'  in 3 years,
∴  '3X' becomes ' 9X' in (3 + 3) = 6 years.

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