A certain sum at a certain rate of simple interest amounts to rs.1200 in 4 years and rs.1450 in 9 years.Find the sum and rate of interest?

(a)Rs.500.10%
(b)Rs.800.8%
(c)Rs.900.7%
(d)Rs.1000.5%

• d) Rs1000, 5%
  
  Let P be the sum and R rate
  
  A = P + PNR/100
  1200 = P + 4*PR/100 ---(1)
  1450 = P + 9*PR/100 ---(2)
  
  eqn (1)/(2)
  
  1200/1450 = (1+4R/100)/(1+9R/100)
  24/29 = (100+4R)/(100+9R)
  24*(100+9R) = 29*(100+4R)
  100R = 500
  R = 5%
  
  1200 = P + 4*PR/100
  1200 = P + 4*5*P/100
  P = 1200*5/6
  = 1000
  
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