Question

fraction becomes 9/11 if 2 is added to both and numerator and denominator if 3 is added to both the nominator and denominator it becomes 5 by 6 find the fraction​

Answer 1

Solution

Given :-

• fraction becomes 9/11 if 2 is added to both and numerator and denominator.
• if 3 is added to both the numerator and denominator it becomes 5 by 6

Find :-

• The required Fraction

Explantion

Let

==> Numerator be x

And,

==> Denominator be y.

Case 1.

(fraction becomes 9/11 if 2 is added to both and numerator and denominator)

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

==> 11 × (x + 2) = 9 × ( y + 2)

==> 11x - 9y = 18 - 22

==> 11x - 9y = -4_____________(1)

And,

Case 2.

(3 is added to both the nominator and denominator it becomes 5 by 6)

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

==> 6 × (x + 3) = 5 × ( y + 3)

==> 6x - 5y = 15 - 18

==> 6x - 5y = -3___________(2)

Multiply by 9 in equ(2) & 5 in equ(1)

==> 55x - 45y = -20_________(3)

And,

==> 54x - 45y = -27__________(4)

Sub. equ(3) & equ(4)

==> 55x - 54x = -20 + 27

==> x = 7

keep in equ(3)

==> 55×7 - 45y = -20

==> -45y = -20 - 385

==> 45y = 405

==> y = 405/45

==> y = 9

Hence

• Required fraction will be (x/y) = 7/9

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