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If the numerator of a fraction is multiplied by 2 and the denominatoris reduced by 5 the fraction becomes 6/5. And, if the denominator is doubledand the numerator is increased by 8, the fraction becomes 2/5. Find thefraction. |
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Answer» Let the required fraction be ` (x)/( y)`. Then, `(2x )/( y - 5) = (6)/(5) rArr 10 x = 6 ( y - 5) ` ` " " rArr 10 x - 6y = - 30 ` `" " rArr 5 x - 3y = - 15 " " ` … (i) and ` (x + 8 )/( 2y ) = ( 2 ) /( 5) rArr 5 ( x + 8) = 4 y ` ` " " rArr 5 x - 4y = - 40 " " `... (ii) On subtracting (ii) from (i), we get `y = 25` Putting ` y = 25 ` in (i), we get ` 5x - ( 3 xx 25) = - 15 rArr 5x - 75 = - 15 rArr 5 x = 60 rArr x = 12.` ` therefore x = 12 and y = 25 ` Hence, the required fraction is ` (12)/( 25)` |
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