the sum of the denomirator and numerator of a fraction is 40. if 1 is added to both the numerator and the denomirator, the fraction becomes 3/4.find the fration
Answers
Solution :-
Let the numerator and denominator be x and y respectively.
Case I : The sum of the denomirator and numerator of a fraction is 40.
=> x + y = 40
=> x = 40 - y _____(i)
Case II : 1 is added to both the numerator and the denomirator, the fraction becomes 3/4.
=> (x + 1)/(y + 1) = 3/4
=> 4(x + 1) = 3(y + 1)
=> 4x + 4 = 3y + 3
=> 4(40 - y) + 4 = 3y + 3 [from equation (i)]
=> 160 - 4y + 4 = 3y + 3
=> - 4y - 3y = 3 - 4 - 160
=> - 7y = -161
=> y = - 161/-7 = 23
Substituting the value of y in equation (i),
=> x = 40 - 23 = 17
Hence,
Fraction = x/y = 17/23
Answer:
let the numerator be x
denomenator be y
so, x + y = 40. 1eq
and. x+ 1/y+ 1=3/4. 2 eq
cross multiply
(x+1)4=(y+1)3
4x+4=3y+3
4x-3y =3-4
4x-3y=-1
multiple eq1 by 3
3x +3y = 120
4x - 3y = -1
on elimination
7x= 119
x=17
so y=23
pls mark me the brainiest if it helped u