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Math Topic - SI

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Helpful Notes for students who are preparing for competitive exams.

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    PBI Rules and Formulae: PBI INSTITUTE Simple Interest 1. 2. 3. 1. Principal : The money borrowed or lent out for a certain period is called the principal or the sum. Interest : Extra money paid for using other's money is called interest. Simple Interest (S.I.) : If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest. Let the principal = P, Rate = R% per annum (p.a) and Time = T years. Then , s.l. = (P x Rx T/ 100) EXERCISE A man took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was A. Rs. 2000 C. Rs. 15,000 Solution Principal B. D. < = > RS. 15,000. Rs. 10,000 Rs. 20,000 2. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is A. 50/0 c. 80/0 Solution Let the rate be p.a. Then, B. 70/0 D. 100/0 RYO (5000xRx2/100) + (3000xRx4/100) 2200 Rate 3. A money lender finds that dues to a fall in the annual rate of interest from 8% to 7x3/4%, his yearly income diminishes by Rs. 61.50. His capital is A. Rs. 22,400 C. Rs. 24,600 B. Rs. 23,800 D. Rs. 26,000
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    x. Then, 4. PBI Solution Let the capital be Rs. = Rs. 117. = Rs. 698 PBI INSTITUTE (x = 61.50. - 31x < = > X = 24600. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9. p.c.p.a in 5 years. What is the sum? A. Rs. 4462.50 C. Rs. 8900 Solution Principal B. Rs. 8032.50 D. Rs. 8925 5. Rs. (401625/45) < = > RS. 8925. A sum of money at simple interest amounts to Rs.815 in 3 years and to Rs. 854 in 4 years. The sum is A. Rs. 650 C. Rs. 698 Solution S.I. for 1 year S.I. for 3 year Principal B. Rs. 690 D. Rs. 700 = Rs.(854 - 815) = Rs. 39 = Rs.(39x3) = Rs. (815 - 117) 6. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest? A. 3.5 years C. 4.5 years Solution B. 4 years D. 5 years Time 7. < = > 4 years. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned? A. Rs. 35 C. Rs. 350 Solution B. Rs. 245 D. cannot be determined We need to know the S.I., principal and time to find the rate. Since the principal is not given, so data is inadequate. 8. What is the present worth of Rs. 132 due in 2 years at 5% simple interest per annum?
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    A. c. Solution PBI = Rs. 300 = Rs. 120. = Rs. 600 PBI INSTITUTE Rs. 112 Rs. 120 B. D. Rs. 118.80 Rs. 122 Let the present worth be Rs.x. Rs.(132 - x). 9. (XX 5 x 2/100) 132 -x lox = 13200 - = 13200 120 An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes A. 100/0 c. 10.5% Solution Let the sum be Rs. S.I. for first 6 months S.I. for last 6 months So,amount at the end of 1 year = Rs.(100 + 5 + Rs.110.25 Effective = 10.25%. rate(110.25-100) 10. A sum of money lent out at simple interest amounts to Rs. 720 after 2 years and to Rs. 1020 after a further period of 5 years. The sum is B. 10.25% D. None of these 100. = Rs. 5.25. A. Rs. 500 C. Rs. 700 Solution S.I. for 5 year S.I. for 2 year Principal B. Rs. 600 D. Rs. 710 11. = Rs.(1020 - 720) = Rs.(300/5x2) = Rs. (720 - 120) A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? B. 40/0 Solution s.l. - Rs. (15500 - 12500)
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    PBI PBI INSTITUTE Rate 12. = Rs. 3000. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is A. 50/0 D. 15% Solution S.I. for 3 year S.I. for 5 year Principal = Rs.(12005 - 9800) = Rs. 2205. = Rs.(2205/3 = Rs. 3675. = Rs. (9800 - 3675) = Rs. 6125. Hence, rate = / 12%. 13. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest? A. 3.5 years C. 4.5 years B. 4 years D. 5 years Solution Time 14. = (100 x 81 / 450 x 4.5)years (8100/2025)years < = > 4 years. A person takes a loan of Rs. 200 at 5% simple interest. He returns Rs. 100 at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay A. Rs. 105 C. Rs. 115 Solution Amount to be paid B. Rs. 110 D. Rs. 115.50 - Rs.(100+200x5x1/100 + 115. 15. At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years? A. c. 2% 6% B. 40/0 Solution Let sum = x Time Then, s.l = 10 years. Rate 16. The simple interest on Rs. 1820 from march 10, 2003 to may 21, 2003 at 7x1/2% rate will be
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    PBI IN A. c. Solution Time B. D. PBI INSTITUTE Rs. 27.30 Rs. 29 s.l 17. Rs. 22.50 Rs. 28.80 = (22+30+21) days days. 1/5 year. 27.30. At what percent per annum will a sum of money double in 16 years? A. 5

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