Question

5. A Fraction become 3/11, if 2 is added to both the numerator and the denominator. If 3 is
added to both the numerator and the denominator, it becomes 5/6 Find the fraction.​

Answer 1

Correct Question :- A Fraction become 9/11, if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 5/6 Find the fraction. { Note :- if we take 3/11, value of N and D both are coming in fraction and in negative. i tried to solved it .}

Solution :-

Let us assume that, the Original fraction is N/D , where N is numerator of the fraction and D is denominator of the fraction.

Case 1) :- The fraction become 3/11, if 2 is added to both the numerator and the denominator.

So,

→ (N + 2) / (D + 2) = 9/11

cross - Multiply,

→ 11(N + 2) = 9(D + 2)

→ 11N + 22 = 9D + 18

→ 11N - 9D = 18 - 22

→ 11N - 9D = (-4) -------------- Eqn.(1)

Case 2) :- If 3 is added to both the numerator and the denominator, it becomes 5/6.

So,

→ (N + 3) / (D + 3) = 5/6

cross - Multiply,

→ 6(N + 3) = 5(D + 3)

→ 6N + 18 = 5D + 15

→ 6N - 5D = 15 - 18

→ 6N - 5D = (-3) -------------- Eqn.(2)

Multiply Eqn.(1) by 5 and Eqn.(2) by 9 , and than subtracting Eqn.(2) from Eqn.(1) , we get,

→ 5(11N - 9D) - 9(6N - 5D) = 5(-4) - 9(-3)

→ 55N - 54N - 45D + 45D = (-20) + 27

→ N = 7 .

Putting value of N in Eqn.(2),

→ 6 * 7 - 5D = (-3)

→ 5D = 42 + 3

→ 5D = 45

→ D = 9.

Hence, Original fraction is N/D = 7/9.

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