Question

If the numerator and denominator of a fraction are increased and decreased by 1 respectively, then it becomes 12/11 if the numerator and denominator are increased and decreased by 3 respectively then it becomes 14/9 find the fraction.

Answer needed. ​

Answer 1

Question ↷

• If the numerator and denominator of a fraction are increased and decreased by 1 respectively, then it becomes 12/11 if the numerator and denominator are increased and decreased by 3 respectively then it becomes 14/9 find the fraction.

Answer↷

• 11/12

Solution ↷

Let the numerator be x & denominator be y then,

ATQ,

x+1/y-1=12/11

11x+11=12y-12

11x-12y+11+12=0

11x-12y+23=0....(1)

&

x+3/y-3=14/9

9x+27=14y-42

9x-14y+27+42=0

9x-14y+69=0....(2)

Multiplying eq . 1 by 9 & eq. 2 by 11

We get,

99x-108y+207=0....(3)

99x-154y+759=0....(4)

Subtracting eq. 4 by eq. 3

99x-108y+207=0

99x-154y+759=0

______________

0 + 46y - 552 =0

______________

46y= 552

________

y=552/46

________

y=12

____

putting the value of y in eq. 1,

11x-12y+23=0

11x-12*12+23=0

11x-144+23=0

11x-121=0

11x=121

x=121/11

x=11

So, y = 12 & x = 11 & the fraction is 11/12

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-lyricalblues