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A fraction becomes ` (1)/(3)`, if 2 is added to both of its numerator and denominator. If 3 is added to both of its numerator and denominator then it becomes ` ( 2)/(5)`. Find the fraction. |
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Answer» Let the required fraction be `(x)/(y) `. Then, ` (x+ 2 )/( y + 2 ) = (1)/(3) rArr 3x + 6 = y + 2 ` ` " " rArr 3x - y = - 4 " " `… (i) Also, ` ( x + 3 ) /( y + 3 ) = ( 2) /( 5) rArr 5x + 15 = 2y + 6 ` `" " rArr 5x - 2y = - 9 " " `... (ii) Multiplying (i) by 2 and subtracting (ii) from the result, we get ` 6 x - 5 x = - 8 + 9 rArr x = 1 ` Putting x = 1 in (i), we get ` 3- y = - 4 rArr y = 7`. Thus, ` x= 1 and y = 7` Hence, the required fraction is ` (1)/(7)` |
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