The denominator of a fraction is 2more than thrice it's numerator. If the numerator as well as the denominator are increase by 1 the fraction become 1/3.What is the original fraction?
Answers
Answer:
Given :-
The sum of numerator and denominator of a fraction is greater by 1 than thrice the numerator is decreased by 1 then the fraction reduced to 1/3.
To Find :-
What is the fraction.
Solution :-
Let, the fraction be x/y
According to the question,
➣ The sum of numerator and denominator of a fraction is greater by 1 than thrice the numerator.
⇒ x + y = 3x + 1
⇒ y = 3x - x + 1
⇒ y = 2x + 1 .......... equation no (1)
➣ Denominator is decreased by 1 than the fraction reduced by 1/3.
⇒ x - 1/y = 1/3
⇒ 3(x - 1) = y
⇒ 3x - 3 = y
⇒ 3x - y = 3 ......... equation no (2)
➣ Now, putting the value of x from equation no (1) in equation no (2) we get,
⇒ 3x - y = 3
⇒ 3x - (2x + 1) = 3
⇒ 3x - 2x - 1 = 3
⇒ x = 3 + 1
➠ x = 4
➣ Again, putting the value of x in the equation no (1) we get,
⇒ y = 2x + 1
⇒ y = 2(4) + 1
⇒ y = 8 + 1
➥ y = 9
Hence, the required fraction will be,
↦ x/y
➽ 4/9
∴ The fraction will be 4/9 .