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COMPLEX PROBLEMS
1. A certain sum of money amounts t 1680 in 3yrs & it becomes 1920 
       in 7 yrs .What is the sum. 
Sol:-                              3 yrs - - - - - - - - - - - - - 1680 
                                      7 yrs - - - - - - - - - - - - - 1920 
                   then,           4 yrs - - - - - - - - - - - - - 240 
                                       1 yr  - - - - - - - - - - - - -   ? 
                              (1/4) * 240 = 60 
                S.I in 3 yrs = 3*60 = 18012 
                           Sum = Amount - S.I 
                                    = 1680 - 180 
                                    = 1500 
           we get the same amount if we take S.I in 7 yrs 
                     I.e., 7*60 =420 
                            Sum = Amount - S.I 
                                     = 1920 - 420 
                                     = 1500     
 
2. A Person takes a loan of Rs 200 at 5% simple Interest. He returns Rs.100 at  the end of 1 yr. In order to clear his dues at the end of 2yrs ,he would pay: 
Sol:-                           Amount to be paid 
                            = Rs(100 + (200*5*1)/100 + (100*5*1)/100) 
                            = Rs 115 
 

3. A Man borrowed Rs 24000 from two money lenders.For one loan, he    
      paid 15% per annum and for other 18% per annum .At the end of one    
      year,he paid Rs.4050.How much did he borrowed at each rate? 
Sol:-                  Let the Sum at 15% be Rs.x 
                          & then at 18% be Rs (24000-x) 
                               P1 = x                    R1 = 15 
                               P2 = (24000-x)      R2 = 18 
 
                  At the end of ine year T = 1 
                          (P1*T*R1)/100 + (P2*T*R2)/100 = 4050 
                          (x*1*15)/100 + ((24000-x)*1*18)/100 = 4050 
                                         15x + 432000 - 18x = 405000 
                                       x = 9000 
              Money borrowed at 15% = 9000 
              Money borrowed at 18% = (24000 - 9000) 
                                    = 15000 
 
4. What annual instalment will discharge a debt of Rs. 1092 due in 3 years 
       at 12% Simple Interest ? 
Sol:-                      Let each instalment be Rs x  
 
                           (x + (x * 12 * 1)/100) + (x + (x * 12 * 2)/100) + x = 1092 
                           28x/25 + 31x/25 + x =1092 
                          (28x +31x + 25x) = (1092 * 25) 
                                                84x = 1092 * 25 
                                                 x = (1092*25)/84 = 325 
                                Each instalement  =  325 


5. If x,y,z are three sums of money such that y is the simple interest on x,z  
       is the simple interest on y for the same time and at the same rate of   
       interest ,then we have: 
Sol:-                     y  is simple interest on x, means 
                                                y = (x*R*T)/100 
                                            RT = 100y/x 
                            z   is simple interest on y, 
                                               z = (y*R*T)/100 
                                            RT = 100z/y 
                                      100y/x = 100z/y 
                                           y * y = xz 
 
6.A Sum of Rs.1550 was lent partly at 5% and partly at 5% and partly at 8% p.a  Simple interest .The total interest received after 3 years was Rs.300.The ratio of the money lent at 5% to that lent at 8% is: 
Sol:-                           Let the Sum at 5% be Rs x 
                                           at 8% be Rs(1550-x) 
                         (x*5*3)/100 + ((1500-x)*8*3)/100 = 300 
                                  15x + 1500 * 24 - 24x = 30000 
                                                     x = 800  
                             Money at 5%/ Money at 8% = 800/(1550 - 800) 
                                                      = 800/750 = 16/15 
 
7. A Man invests a certain sum of money at 6% p.a Simple interest and another  sum at 7% p.a Simple interest. His income from interest after 2 years was  Rs 354 .one fourth of the first sum is equal to one fifth of the second sum.The total sum invested was: 
Sol:-                             Let the sums be x & y 
                                                R1 = 6     R2 = 7 
                                                T = 2 
                            (P1*R1*T)/100 + (P2*R2*T)/100 = 354 
                          
                            (x * 6 * 2)/100  + (y * 7 * 2)/100 =  354 
                                                    6x + 7y = 17700 ———(1) 
           also one fourth of the first sum is equal to one 
                 fifth of the second sum 
                            x/4 = y/5 => 5x - 4y = 0 —— (2) 
    By solving 1 & 2 we get, 
                             x = 1200       y = 1500 
                                Total sum = 1200 +1500 
                                          = 2700      
 
8. Rs 2189 are divided into three parts such that their       
      amounts after 1,2& 3 years respectively may be equal ,the rate of    
      S.I being 4% p.a in all cases. The Smallest part is: 
Sol:-               Let these parts be x,y and[2189-(x+y)] then, 
                        (x*1*4)/100 = (y*2*4)/100 =  (2189-(x+y))*3*4/100 
                                      4x/100 = 8y/100 
                                             x = 2y 
              By substituting values 
                       (2y*1*4)/100 = (2189-3y)*3*4/100 
                                      44y = 2189 *12 
                                          y = 597 
                      Smallest Part = 597 
 
9. A man invested 3/3 of his capital at 7% , 1/4 at 8% and the remainder at 10% 
      If his annual income is Rs.561. The capital is: 
Sol:-                         Let  the capital be Rs.x 
 
            Then, (x/3 * 7/100 * 1) + ( x/4 * 8/100 * 1)
                                        + (5x/12 * 10/100 * 1) = 561 
 
                                7x/300 + x/50 + x/24 = 561 
                                                     51x = 561 * 600 
                                                       x = 6600

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