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- Question
Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
Options- A. Rs. 1550
- B. Rs. 1650
- C. Rs. 1750
- D. Rs. 2000
- Correct Answer
- Rs. 1750
ExplanationC.I. = Rs. [ 4000 x ❨ 1 + 10 ❩ 2 - 4000 ] 100 = Rs. ❨ 4000 x 11 x 11 - 4000 ❩ 10 10 = Rs. 840. ∴ Sum = Rs. ❨ 420 x 100 ❩ = Rs. 1750. 3 x 8
Compound Interest problems
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- 1. The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
Options- A. 8
- B. 10
- C. 12
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 8
Explanation:
[ 15000 x ❨ 1 + R ❩ 2 - 15000 ] - ❨ 15000 x R x 2 ❩ = 96 100 100 ⟹ 15000 [ ❨ 1 + R ❩ 2 - 1 - 2R ] = 96 100 100 ⟹ 15000 [ (100 + R)2 - 10000 - (200 x R) ] = 96 10000 ⟹ R2 = ❨ 96 x 2 ❩ = 64 3 ⟹ R = 8.
∴ Rate = 8%.
- 2. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
Options- A. 2
- B.
2 1 2 - C. 3
- D. 4 Discuss
Correct Answer: 2
Explanation:
Amount = Rs. (30000 + 4347) = Rs. 34347.Let the time be n years.
Then, 30000 ❨ 1 + 7 ❩ n = 34347 100 ⟹ ❨ 107 ❩ n = 34347 = 11449 = ❨ 107 ❩ 2 100 30000 10000 100 ∴ n = 2 years.
- 3. There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
Options- A. Rs. 2160
- B. Rs. 3120
- C. Rs. 3972
- D. Rs. 6240
- E. None of these Discuss
Correct Answer: Rs. 3972
Explanation:
Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.∴ R = ❨ 100 x 60 ❩ = 10% p.a. 100 x 6 Now, P = Rs. 12000. T = 3 years and R = 10% p.a.
∴ C.I. = Rs. [ 12000 x { ❨ 1 + 10 ❩ 3 - 1 ] ] 100 = Rs. ❨ 12000 x 331 ❩ 1000 = 3972. - 4. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
Options- A. 3
- B. 4
- C. 5
- D. 6 Discuss
Correct Answer: 4
Explanation:
P ❨ 1 + 20 ❩ n > 2P ⟹ ❨ 6 ❩ n > 2. 100 5 Now, ❨ 6 x 6 x 6 x 6 ❩ > 2. 5 5 5 5 So, n = 4 years.
- 5. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
Options- A. Rs. 120
- B. Rs. 121
- C. Rs. 122
- D. Rs. 123 Discuss
Correct Answer: Rs. 121
Explanation:
∴ C.I. = Rs. (3321 - 3200) = Rs. 121Amount = Rs. [ 1600 x ❨ 1 + 5 ❩ 2 + 1600 x ❨ 1 + 5 ❩ ] 2 x 100 2 x 100 = Rs. [ 1600 x 41 x 41 + 1600 x 41 ] 40 40 40 = Rs. [ 1600 x 41 ❨ 41 + 1 ❩ ] 40 40 = Rs. [ 1600 x 41 x 81 ] 40 x 40 = Rs. 3321. - 6. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
Options- A. 625
- B. 630
- C. 640
- D. 650 Discuss
Correct Answer: 625
Explanation:
Let the sum be Rs. x. Then,C.I. = [ x ❨ 1 + 4 ❩ 2 - x ] = ❨ 676 x - x ❩ = 51 x. 100 625 625 S.I. = ❨ x x 4 x 2 ❩ = 2x . 100 25 ∴ 51x - 2x = 1 625 25 ⟹ x = 625.
- 7. A, B and C enter into a partnership in the ratio 7⁄2 : 4⁄3 : 6⁄5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 21,600, then B's share in the profit is:
Options- A. Rs. 2100
- B. Rs. 2400
- C. Rs. 3600
- D. Rs. 4000 Discuss
Correct Answer: Rs. 4000
Explanation:
Ratio of initial investments = ❨ 7 : 4 : 6 ❩ = 105 : 40 : 36. 2 3 5 Let the initial investments be 105x, 40x and 36x.
∴ A : B : C = ❨ 105x x 4 + 150 x 105x x 8 ❩ : (40x x 12) : (36x x 12) 100 = 1680x : 480x : 432x = 35 : 10 : 9.
Hence, B's share = Rs. ❨ 21600 x 10 ❩ = Rs. 4000. 54 - 8. A starts business with Rs. 3500 and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B's contribution in the capital?
Options- A. Rs. 7500
- B. Rs. 8000
- C. Rs. 8500
- D. Rs. 9000 Discuss
Correct Answer: Rs. 9000
Explanation:
Let B's capital be Rs. x.Then, ❨ 3500 x 12 = 2 ❩ 7x 3 ⟹ 14x = 126000
⟹ x = 9000.
- 9. A and B started a business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options- A. Rs. 7500
- B. Rs. 9000
- C. Rs. 9500
- D. Rs. 10,000 Discuss
Correct Answer: Rs. 7500
Explanation:
A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.∴ B's share = Rs. ❨ 25000 x 3 ❩ = Rs. 7,500. 10 - 10. Aman started a business investing Rs. 70,000. Rakhi joined him after six months with an amount of Rs.. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
Options- A. 7 : 6 : 10
- B. 12 : 15 : 16
- C. 42 : 45 : 56
- D. Cannot be determined Discuss
Correct Answer: 12 : 15 : 16
Explanation:
Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.
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