Math, asked by abhijayperiye200722, 1 month ago

When we add 1 to the numerator of a fraction and simplify it we get 2/3.when add 1 to the denominator and simplify it we get 1/2.which is the fraction?​

Answers

Answered by mubs16
1

Step-by-step explanation:

let the the fraction be x/y.

Adding 1 to numerator gives 2/3

(x+1) /y = 2/3

3(x+1) = 2y

3x + 3 = 2y

Adding 1 to denominator gives 1/2

x/(y+1) = 1/2

2x = y + 1

2x - 1 = y

substituting y = 2x - 1 in above expression

3x + 3 = 2y

3x + 3 = 2(2x - 1)

3x + 3 = 4x -2

3x + 5 = 4x

5 = 4x - 3x

5 = x

therefore y = 2x - 1 = 10 - 1 = 9 (as x = 5 from above)

Fraction is x/y = 5/9

Answered by RvChaudharY50
1

Answer :-

Let us assume that, the fraction is N/D .

so,

case 1) :-

→ N+1/D = 2/3

cross - multiply,

→ 3N + 3 = 2D

→ 3N - 2D = (-3) --------- Eqn.(1)

case 2) :-

→ N / D + 1 = 1/2

→ 2N = D + 1

→ 2N - D = 1 ------------ Eqn.(2)

multiply Eqn.(2) by 2 and subtracting from Eqn.(1)

→ (3N - 2D) - 2(2N - D) = (-3) - 2*1

→ 3N - 4N - 2D + 2D = -3 - 2

→ - N = - 5

→ N = 5

then, putting value of N in Eqn.(2)

→ 2 * 5 - D = 1

→ 10 - 1 = D

→ D = 9

therefore,

→ Required fraction = N/D = (5/9) (Ans.)

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