Question

A fraction becomes , If 2 is added to both
the numerator and the denominator . If , 3 is

added to both the numerator and the
denominator it becomes , find the fraction .​

Answer 1

Correct Question :-

A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If 3 is added to both numerator and denominator, it becomes 5/6. Find the fraction.

Solution :-

Given,

• A fraction becomes 9/11 if 2 is added to both the numerator and the denominator.

• If 3 is added to both the numerator and the denominator, the same fraction becomes 5/6.

To Find,

• The Fraction.

Solution,

Let,

• The Numerator = x.

• Denominator = y.

According To The Given Condition,

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

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

=> 11x + 22 = 9y + 18.

=> 11x – 9y = 18 – 22.

=> 11x – 9y = -4.

=> 11x – 9y + 4 = 0.

=> 11x = 9y – 4.

=> x = (9y – 4)/11. – (i)

And, Also,

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

=> 6x – 5y = 15 – 18.

Put the value of x.

=> 6(9y – 4)/11 – 5y = –3.

=> y + 24 = 33.

=> y = 33 – 24.

=> y = 9.

Now, Calculating the value of x.

=> x = (9y – 4)/11.

=> x = (9(9) – 4)/11.

=> x = (81 – 4)/11.

=> x = 77 ÷ 11.

=> x = 7.

So, The Original Fraction = x/y = 7/9.

Answer 2

The Right Question :-

A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If 3 is added to both numerator and denominator, it becomes 5/6. Find the fraction.

Answer :-

• The required fraction is $7/9$

Given :-

• 2 is added to both the numerator and the denominator .
• If , 3 is added to both the numerator and the denominator it becomes 9/11.

To find :-

• what is the required fraction ?

Solution :-

➤ Let the fraction be x/y

( 1 )condition = X + 2 /y + 2 = 9/11

( 2 ) condition = x + 3/ y + 3 = 5/6

Now ,

⇒ 11x + 22 = 9y + 18.

⇒ 11x - 9y = - 4 ------ (1)

⇒ 6x + 18 = 5y + 15

⇒ 6x - 5y = -3 --------(2)

From (1) and (2)

⇒ 5y = 6x + 3

⇒ y = 6x + 3 /5

➤ Put y = 6x + 3 /5 in eqn (1) .

⇒ 11x - 9 [ 6x + 3/5 ] = - 4

⇒ 55x - 54x - 27 = - 20

⇒ x = - 20 + 27

⇒ x = 7 .

Now,

➤ Put ( x = 7 ) in eqn .1

1 × 7 - 9y = - 4

⇒ - 9y = -4 - 77

⇒ – 9y = – 81

⇒ y = 81/9

⇒ y = 9

Hence , the required fraction is $7/9$

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