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$A fraction becomes 911, if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 56. Find the fraction.$
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Answer 1

Step-by-step explanation:

let the fraction be x/y

(x+2)/(y+2) = 911

(x+2) = 911(y+2)

x+2 = 911y + 1822

x+2-1822 = 911y

x-1820 = 911y

x-1820-911y = 0

or

x-911y-1820 = 0 (eqn. no. 1)

(x+3)/(y+3) = 56

(x+3) = 56(y+3)

x+3 = 56y + 168

x+3-168 = 56y

x-165 = 56y

x-165-56y = 0

or

x-56y-165 = 0 (eqn. no. 2)

substracting eqn. no. 1 and eqn. no. 2

= (x-911y-1820 = 0) - ( x-56y-165 = 0)

= x-911y-1820 - x+56y+165 = 0

= - 855y - 1655 = 0

= -855y = 1655

= y = 1655/(-855)

y = - 331/171

putting y = 331/171 in eqn. no. 1

x-911y-1820 = 0

x-911(-331/171) - 1820 = 0

x + 301541/171 - 1820 = 0

171x + 301541 - 311220 = 0

171x - 9679 = 0

171x = 9679

x = 9679/171

x/y = (9679/171)/(- 331/171)

x/y = (9679×171)/(171×(-331))

x/y = 9679/(-331)

Hence, the fraction is - 9679/331