Question

The numerator of a fraction is 2 less than its denominator if 3 is subtracted from the numerator and from the denominator the new fraction of 10 is 3/4. find the fraction

Answer 1

Answer:

Given :-

• The numerator of a fraction is 2 less than its denominator.
• If 3 is subtracted from numerator and from the denominator, the new fraction obtained is 3/4.

Find Out :-

• What is the fraction ?

Solution :-

Let the numerator of the fraction be 'x' and Denominator be 'y'

FRACTION = x/y

CASE:- 1)

◆ The numerator of a fraction is 2 less than its denominator.

According to question:-

➜ x = y –2....❶

CASE:- 2)

◆ If 3 is subtracted from numerator and from the denominator, the new fraction obtained is 3/4.

According to question:-

➜ $\sf \bigg(\dfrac{x - 3}{y - 3}\bigg) =\: \dfrac{3}{4}$

Use cross product

➜ 4(x–3) = 3(y–3)

➜ 4x –12 = 3y –9

➜ 4x –3y = –9+12

➜ 4x –3y = 3....❷

Put the value of 'x' from equation 1) in equation 2)

➜ 4(y–2) –3y = 3

➜ 4y –8 –3y = 3

➜ y = 3+8

⠀⠀⠀⠀ ❛ y = 11 ❜

Put the value of 'y' in equation 1)

➜ x = 11 –2

⠀⠀⠀⠀ ❛ x = 9 ❜

➙ NUMERATOR = x = 9

➙ DENOMINATOR = y = 11

✯ FRACTION = 9/11

Hence, the fraction formed is 9/11.