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Compound Interest - Aptitude Questions and Answers - RejinpaulPlacement




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Directions: (57 to 63)
Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is/are sufficient to answer the given question. Read both the statements and
Given answer (a) if the data in statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Given answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question
Given answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question
Given answer (d) if the data even in both Statement I and II together are not sufficient to answer the questions
Given answer (e) if the data in both Statement I and II together are necessary to answer the question.

57.
What is the rate of compound interest? [Bank P.O. 2003]

I. The principal was invested for 4 years.
II. The earned interest was Rs. 1491.
Answer & Solution
Answer: d) if the data even in both Statement I and II together are not sufficient to answer the questions

Solution:   Let Principal = Rs. P and Rate = R% p.a. The,
Amount = Rs. P [1 + (R/100)]^4

C.I. = P{[1 + (R/100)]^4 - 1}
=> P[{1 + (R/100)}^4 - 1] = 1491

Clearly, it does not give the answer.

Correct answer is (d).
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58.
What will be the compound interest? [Bank P.O. 1999]

I. Rs. 200 were borrowed for 192 months at 6% compounded annually.
II.Rs. 200 were borrowed for 16 years at 6%.
Answer & Solution
Answer: c) if the data either in Statement I or in Statement II alone are sufficient to answer the question

Solution:   I. Amount = Rs. [200 * {1 + (6/100)}^16]

II. Amount = Rs. [200 * {1 + (6/100)}^16 ]

Thus, I as well as II gives the answer.

Correct answer is (c)
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59.
What is the compound interest earned by Robert at the end of 2 years?

I. Simple interest at the same rate for one year is Rs. 1020 and the rate of interest is 12 p.c.p.a.
II. The amount invested is Rs. 8500.
Answer & Solution
Answer: a) if the data in statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

Solution:   I. S.I = Rs. 1020, R = 12% p.a. and T = 1 year.

P = [(100 * S.I)/(R * T)]
=> P = Rs. [(100 * 1020)/(12 * 1)] = Rs. 8500

C.I. for 2 years = Rs. [8500 * {[1 + (12/100)]^2 - 1}]

II gives, only P and T.
II alone does not give the answer.

Correct answer is (a).
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60.
What is the total compound interest accrued on a sum of money after 5 years?

I. The sum was Rs. 20,000.
II. The total amount of simple interest on the sum after 5 years was Rs. 4000.
Answer & Solution
Answer: e) if the data in both Statement I and II together are necessary to answer the question.

Solution:   Given : Time = 5 years.

I gives : Sum = Rs. 20000
II gives : S.I = Rs. 4000.

Let the rate be R% p.a. Then,
R = [(100 * S.I.)/(P * T)] = [(100 * 4000)/(5 * 20000)] = 4% p.a.

C.I. = Rs. [20000 * {[1 + (4/100)]^5 - 1]

Both I and II are needed to get the answer.
So, the correct answer is (e)
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61.
What was the total compound interest on a sum after 3 years? [Bank P.O. 2003]

I. The interest after one year was Rs. 100 and the sum was Rs. 1000.
II. The difference between simple and compound interest on a sum of Rs. 1000 at the end of 2 years was Rs. 10
Answer & Solution
Answer: c) if the data either in Statement I or in Statement II alone are sufficient to answer the question

Solution:   I gives : P = Rs. 1000 and S.I. for 1 year = Rs. 100.

Rate = [(100 * S.I.)/(P * T)] = [(100 * 100)/(1000 * 1)] = 10% p.a.
Thus, P = Rs. 1000, T = 3 years and R = 10% p.a.

C.I. may be obtained.

II. Sum = Rs. 1000, [C.I. - S.I.] for 2 years = Rs. 10.

Let the rate be R% p.a.

1000 * [{1 + (R/100)}^2 - 1] - [(1000 * R * 2)/100] = 10

From this, we can find R.

Thus, P, T and R are given and therefore C.I. may be calculated.
Thus, I alone as well as II alone is sufficient to get the answer.

Correct answer is (c).
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62.
An amount of money was lent for 3 years. What will be the difference between the simple and the compound interest earned on it at the same rate?

I. The rate of interest was 8 p.c.p.a.
II. The total amount of simple interest was Rs. 1200
Answer & Solution
Answer: e) if the data in both Statement I and II together are necessary to answer the question.

Solution:   Given : T = 3 years.

I gives : R = 8% p.a.
II gives : S.I. = Rs. 1200

Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.
Difference between C.I and S.I. may be obtained.

So, correct answer is (e).
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63.
What was the rate of interest on a sum of money? [S.B.I.P.O. 1998]

I. The sum fetched a total of Rs. 2522 as compound interest at the end of 3 years.
II. The difference between the simple interest and the compound interest at the end of 2 years at the same rate was Rs. 40.
Answer & Solution
Answer: e) if the data in both Statement I and II together are necessary to answer the question.

Solution:   I gives : C.I. for 3 years = Rs. 2522.
II gives : C.I - S.I for 2 years at same rate is Rs. 40

P[{1 + (R/100)}^3 - 1] = 2522 ....... (i)

P[{1 + (R/100)}^2 - 1] - [(P * R * 2)/100] = 40 ..........(ii)

On dividing (i) by (ii) we get :
{[1 + (R/100)]^3 - 1 } / {[1 + (R/100)]^2 - 1 - (R/50)} = 2522/40
=> {(R^3/1000000) + (3R/100) + (3R^2/10000) } / (R^2/10000) = 1261/20
=> (R/100) + (300/R) = 1201/20
=> R^2 - 6005R + 30000 = 0
=> R^2 - 6000R - 5R + 30000 = 0
=> R(R - 6000) - 5 (R - 6000) = 0
=> (R - 5) (R - 6000) = 0
=> R = 5.

Both I and II are needed to get R.

Correct answer is (e).
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