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MEDIUM PROBLEMS

1. A sum at Simple interest at 13 1/2% per annum amounts to Rs 2502.50 
     after 4 years.Find the sum. 
Sol:- Let Sum be x. then, 
                 S.I = (P*T*R)/100 
                       = ((x*4*27)/(100*2)) 
                       = 27x/100 
       Amount = (x+(27x)/100) 
                     = 77x/50 
        77x/50 = 2502.50 
                  x = (2502.50*50)/77 
                     = 1625 
 
                    Sum = 1625 
 
2. A some of money becomes double of itself in 4 years in 12 years it will become how many times at the same rate. 
Sol:-                 4 yrs  - - - - - - - - -  P 
                       12 yrs - - - - - - - - -   ? 
                  (12/4)* P =3P 
     Amount or Sum = P+3P = 4 times 
 
3. A Sum was put at S.I at a certain rate for 3 years.Had it been put at 2% higher  rate ,it would have fetched Rs 360 more .Find the Sum. 
Sol:-           Let Sum =P 
              original rate = R 
                               T =  3 years 
 
 If 2% is more than the original rate ,it would have fetched 360 more ie., R+2 
 
                    (P*(R+2)*3/100) - (P*R*3)/100 = 360 
                                        3PR+ 6P-3PR = 36000 
                                
                                      6P = 36000 
                                     P = 6000 
                                 Sum = 6000. 
 
4.Rs 800 amounts to Rs 920 in 3yrs at S.I.If the interest rate is increased by 3%,  it would amount to how much? 
Sol:-                 S.I = 920 - 800 = 120 
                     Rate = (100*120)/(800*3) = 5% 
        New Rate = 5 + 3 = 8%   ,  Principal = 800    ,  Time = 3 yrs 
 
                       S.I = (800*8*3)/100 = 192 
 
        New Amount = 800 + 192 
                               = 992 
 
5. Prabhat took a certain amount as a loan from bank at the rate of 8% p.a S.I and gave the same amount to Ashish as a loan at the rate of 12% p.a . If at the end of 12 yrs, he made a profit of Rs. 320 in the deal,What was the original  amount?        
Sol:-      Let the original amount be Rs x.    
                             T = 12 
                             R1 = 8%      R2 = 12%     Profit = 320 
                             P = x 
         (P*T*R2)/100 - (P*T*R1)/100 =320 
              (x*12*12)/100 - (x*8*12)/100 = 320 
                                               x = 2000/3 
                                               x = Rs.666.67 
 
 
6. Simple Interest on a certail sum at a certain rate is 9/16 of the sum . if the 
   number representing rate percent and time in years be equal ,then the rate is. 

Sol:-                          Let Sum = x .Then, 
                                          S.I = 9x/16 
                           Let time = n years & rate = n% 
                                    n = 100 * 9x/16 * 1/x * 1/n 
                                  n * n = 900/16 
                                        n = 30/4 = 7 1/2% 

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