Question

. When the numerator and the denominator of
a fraction are increased by 4 each, the fraction
becomes 2/3. When the denominator is decreased
by 1, it becomes 3/5. Find the fraction.​

Answer 1

Answer:

6/11

Step-by-step explanation:

Let the numerator be x and denominator be y

when the numerator and denominator is increased by 4:

x+4/y+4=2/3

3(x+4)=2(y+4)

3x+12=2y+8

3x-2y=-4 —(1)

when the denominator is decreased by 1:

x/y-1=3/5

5x=3(y-1)

5x=3y-3

5x-3y=-3 —(2)

(1)×3 9x-6y=-12 —(3) (2)×2 10x-6y=-6 —(4) (4)-(3) x=6

From(1), 3×6-2y=-4

18+4=2y

2y=22

y=11

fraction =6/11

Answer 2

Answer:

(x + 2) ÷ (y + 1) = 3/4

Cross multiplication

4 (x + 2) = 3 (y + 1)

4x + 8 = 3y + 3

4x - 3y = -5 → ①

(x - 2) ÷ (y - 1) = 1/2

Cross multiplication

2 (x - 2) = y - 1

2x - 4 = y - 1

2x - y = 3. → ②

Multiply eqn ① by 1 and eqn ② by 2

Eqn ① by 1 - 4x - 3y = -5

Eqn ② by 2 - 4x -2y = 6

Subtract eqn ② from eqn ①

4x - 3y - 4x + 2y = -5 - 6

-y = -11

y = 11

Sub y = 11 in eqn ②

2x - 11 = 3

2x = 14

x = 7

Fraction = x/y = 7/ 11

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