The sum of the numerator and denominator of a fraction is greater by 1 than thrice the numerator. If the numerator is decreased by 1, then the fraction reduced to 1/3. Find the fraction. Solution : The fraction is .........
3 points
Answers
Answer:
The numerator be 'x' and denominator be ' y'
then,
the sum of the numerator and denominator of a fraction is 3 less than the twice is x+y=2y-3 :- x-y+3=0 - equation 1
if the numerator and denominator is decreased by 1 then
x-1/y-1=1/2 :- 2(x-1) = 1(y-1) :- 2x-y-1=0 -equation 2
then equation 1 = equation 2
x-y+3=2x-y-1 :- x=4
from the equation 1
x-y+3=0 :- 4-y+3=0 :- y=7
there fore the fraction is 3/7
Step-by-step explanation:
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 .