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Two numbers are such that the ratio between them us 3:5. If each is increased by 10, the ratio between the new numbers so formed is 5:7. Find the original numbers?
let a and b be the required numbers
given, 
         a:b = 3:5
       ? a/b = 3/5
     ?  5a = 3b
       ie.., 5a-3b=0 ---------------- (1)
also,
         a+10:b+10 = 5:7
       ?   a+10/b+10 = 5/7
       ?    7(a+10) = 5(b+10)
       ?      7a+70 = 5b + 50 
       ?       7a-5b = -20 -----------(2)

(1) × 5 gives
               25a - 15b = 0 -----------(3)
(2) × 3 gives
              21a - 15b = -60 ----------(4)
(3)-(4), we get
              4a = 60
                a = 15
substituting the value of a in (1)
            5×15 - 3b = 0
         ?   3b = 75
         ?     b = 75/3
                    = 25
hence the required numbers are 15 and 25

         


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