Question

The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator if the numerator and the denominator are increased by 3 they become in the ratio 2 is to 3 find the fraction.​

Answer 1

Answer:

Fraction = 5/9

Step-by-step explanation:

Let the numerator be N and Denominator be D.

According to question, given conditions are..

N + D = 2N + 4 and (N + 3)/(D + 3) = 2/3

We have to find the fraction for which we have to find the value of N and D.

→ N + D = 2N + 4

→ - N + D = 4

→ D = 4 + N

Also,

→ (N + 3)/(D + 3) = 2/3

→ 3(N + 3) = 2(D + 3)

→ 3N + 9 = 2D + 6

→ 3N + 3 = 2D

Substitute value of D

→ 3N + 3 = 2(4 + N)

→ 3N + 3 = 8 + 2N

→ N = 5

Substitute value of N in D

→ D = 4 + 5

→ D = 9

Therefore,

Fraction = N/D = 5/9

Answer 2

Question :-- The sum of the numerator and the denominator of a fraction is 4 more than twice the numerator if the numerator and the denominator are increased by 3 they become in the ratio 2 is to 3 find the fraction. ?

Solution :---

Let the original Fraction be N/D, where N is numerator and D is denominator ..

Case 1 :-- The sum of the numerator and the denominator is 4 more than twice the numerator..

So,

→ N + D = 2N + 4

→ 2N - N = D-4

→ N = (D-4) -------------------- Equation (1)

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Case 2:--- if the numerator and the denominator are increased by 3, they becomes in Ratio 2:3 .

So,

→ (N+3) : (D+3) = 2 : 3 .

or,

→ (N+3)/(D+3) = 2/3

Cross-Multiplying we get,

→ 3(N+3) = 2(D+3)

→ 3N + 9 = 2D + 6

→ 2D - 3N = 9-6

→ 2D - 3N = 3 ---------------- Equation (2)

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Now, putting value of Equation (1) in Equation (2) we get,

→ 2D - 3(D-4) = 3

→ 2D -3D +12 = 3

→ -D = 3-12

→ -D = -9

Dividing both sides by 1 ,

→ D = 9.

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Putting this value in Equation (1) now, we get,

→ N = D - 4 = 9-4 = 5

So, original Fraction is N/D = 5/9..