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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 $56$ . The fraction is:

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79

59

89

109

answer is A.

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Detailed Solution

Given, if 2 is added to both the numerator and the denominator, a fraction becomes

911

.
If 3 is added to both the numerator and the denominator it becomes

56

.
Assume fraction =

x y

According to the question,

x + 2 y + 2 = 911

11 (x + 2) = 9 (y + 2)

11 x + 22 = 9 y + 18

11 x − 9 y + 22 − 18 = 0

11 x − 9 y + 4 = 0

11 x − 9 y = − 4

---- 1
Other equation is,

x + 3 y + 3 = 56

6 (x + 3) = 5 (y + 3)

6 x + 18 = 5 y + 15

6 x − 5 y + 18 − 15 = 0

6 x − 5 y + 3 = 0

6 x − 5 y = − 3

---- 2
Using substitution method,
From equation 1,

y = (4 + 11 x) 9

Putting in equation 2,

6 x − 5 4 + 11 x 9 = − 3

54 x − 20 − 55 x = − 3 × 9

54 x − 55 x = − 27 + 20

− x = − 7

x = 7
Now, the value of y

11 x − 9 y = − 4

11 (7) − 9 y = − 4

− 9 y = − 4 − 77

− 9 y = − 81

y = 9
The fraction is

79

.
Hence, option 1 is correct.

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