SIMPLE INTEREST & COMPOUND INTEREST

Q.1 If difference between C.I. & S.I. on a certain sum of money for 2yrs at 5% p.a. is Rs.122. Find the sum ? A) Rs. 14000 B) Rs. 15000 C) Rs. 16000 D) Rs. 17000 Ans. C Shortcut : Sum = Difference * (100)3 / r2 (300+r) Or 122 * (100)3 / 52 (300+5) =Rs. 16000 Q.2 If C.I. on a certain sum for 2 yrs at 12% p.a. is Rs. 1590. What would be the S.I. ? A) Rs. 1400 B) Rs. 1500 C) Rs. 1600 D) Rs. 1700 Ans. B S.I. = R * t / 100 [1 + R/100]2 – 1 * C.I. Or 12 * 2 / 100 [1 + 12/100]2 – 1 * 1590 Thus on solving we get, Rs.1500 Q.3 Gopal lends Rs 3600 on simple interest to Hemant for a period of 5 years. He lends a part of the amount at 4% interest and the rest at 6% and receives Rs. 960 as the amount of interest. How much money did he lend on 4% interest rate?A) 2800B) 2100C) 2400D) 1200Ans. DLet as take amout as x,(3600-x)x*5*4/100 +(3600-x)*5*6/100=960By solving, x=1200 Q.4 UPSC ONLINE ACADEMY wants to buy an air-conditioner for his office. He went to a shop and selects an AC whose price is Rs 12700. The shopkeeper gave him two offers either you pay the full amount of Rs 12700 or pay only Rs 4000 and installment of Rs 3000 per month for the next 3 months just paying Rs. 300 as interest. What is the rate of interest the shopkeeper charged from UPSCONLINE ? A) 23 B) 22 C) 26 D) 21 Ans. D To solve this we have to find a total principle of each monthlike for 1st 12700-4000=87002nd 8700-3000=57003rd 5700-3000=2700 total principal =17100 so use normal formula to find r% per month and take time = 1/12(per month )so r=300*100/17100*(1/12)= 21%      

Q.1 Difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates (in %) ? A) 0.25 B) 0.5 C) 1 D) 2.5 Ans. A Let x & y are the interest rate of two banksThus,According to question,500*x*2/100 – 500*y*2/100 = 2.50Or 10 (x-y) = 2.50x-y = 2.50/10= 0.25 % Q.2 A sum of money doubles itself in 10 yrs at S.I. What is the rate of interest ? A) 8 % B) 9 % C)10 % D) 11 % Ans. C Shortcut: Time *rate=100(principal-1) Or Rate= 100(2-1)/10 =10% Q.3 A certain sum of money amounts to Rs.4720 in 3 yrs at 6 % p.a. S.I. In how many years will it amount to Rs.5680 at the same rate of interest ? A) 4 yrs B) 5 yrs C) 6 yrs D) 7 yrs Ans. D T= 1/r [ ( A2 / A1 * 100 + rt1 ) – 100] 1/6 [5680/4720 100 + 6 * 3 – 100] 1/6 [ 71/59*118-100] =1/6 [142-100] Or 42/6 = 7yrs Q.4 A sum of money doubles itself in 4 yrs at S.I. In how many years will it amount to 8 times ? A) 28 yrs B) 29 yrs C) 30 yrs D) 31 yrs Ans. A Double in 4 yrs Triple in 4*2=8 yrs 4 times in 4*3 = 12 yrs 5 times in 4*4 =16 yrs 6 times in 4*5 = 20 yrs 7 times in 4*6 = 24 yrs 8 times in 4*7 = 28 yrs Q.5 Difference between C.I. & S.I. on a certain sum at 10% p.a for 2 yrs is Rs. 631. Find the sum ? A) 63100 Rs. B) 63200 Rs. C) 63300 Rs. D) 63400 Rs. Ans. A Shortcut : Sum=Difference * (100/R)2 Or 631*100*100 / 10*10 =Rs. 63100      

Q.1 Rs. 4800 becomes Rs. 6000 in 4 yrs at a certain rate of C.I. What will be the sum after 12 yrs ?A) Rs. 9375B) Rs. 9475C) Rs. 9575D) Rs. 9675 Ans. AShortcut:4800 [(6000)12/4 / (4800)12/4-1 ]Or 4800 * (6000)3 / (4800)2Rs. 9375 Q.2 A sum of money doubles itself at C.I. in 15 yrs. In how many yrs will it become 8 times ?A) 45 yrsB) 46 yrsC) 47 yrsD) 48 yrsAns. AP becomes 2p in 15 yrs2p becomes 4p in next 4 yrs4p becomes 8p in next 4 yrsTherefore, 15+15+15 = 45yrs Q.3 Man deposits Rs.5600 in a bank at 3 ¾% annual interest. After 6 months he withdraws Rs. 3200 together with the total interest till now & after the end of the year he withdraw the remaining money. How much does he get as interest ?A) 150B) 160C) 155D) 165Ans. AS.I. of Rs. 5600 for 6 months = 5600 * ½ * 15/4 / 100 = Rs.105He withdraws Rs. 3200 together with interest, then remaining amount = 5600 – 3200 = Rs. 2400S.I. on Rs. 2400 at the rate of 15/4 for ½ year =2400 * ½ * 15/4 / 100 = Rs.45Therefore, total interest = 45 + 105 = 150 Q.4 Sum of money amounts to Rs. 944 in 3 years at S.I. If the rate of interest be raised by 25%, sum amounts to Rs. 980 during the same period. Find the sum & the rate of interest ?A) 4%B) 5%C) 6%D) 7%Ans. C980 – 944 = Rs. 3625 % of interest = 36 * 100 / 25 = 144 Hence interest of three years = Rs. 144Therefore, principal = 944 – 144 = Rs. 800/-Rate = 144 * 100 / 800 * 3 = 6%Hence profit = 132 ¼ – 100= 32 ¼ % Q.5 Simple interest on a certain sum of money for 3 years at 4% is Rs. 303.60. Find the compound interest on the same sum for the same period & at the same rate ?A) Rs. 315.90B) Rs. 316.90C) Rs. 317.90D) Rs. 318.90Ans. AP = 303.60 * 100 / 4 * 3 = Rs. 2530C.I. = p [(1+ R/100)t – 1 ]= 2530 [(1 + 4/100)3 – 1 ] Or 2530 [(26/25)3 – 1]2530 [1951 / 15625 ] = Rs. 315.90