a fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator find the fraction
Answers
Given :-
A fraction becomes 1/3 when 1 is subtracted from the numerator.
It become 1/4 when 8 is added to its denominator.
Solution :-
Let the fraction be x/y
According to the question,
⇒ x–1/y = 1/3
⇒ 3x – y = 3... (i)
⇒ x/y + 8 = 1/4
⇒ 4x – y = 8 ... (ii)
Subtracting equation (i) from equation (ii), we get
⇒ x = 5 ... (iii)
Putting this value in equation (i), we get
⇒ 15 – y = 3
⇒ y = 12
Hence, the fraction is 5/12.
Step-by-step explanation:
let the fraction be n/d
according to first condition
(n-1)/d = 1/3
3(n-1) = d
3n-3 = d _______(i)
according to second condition
n/(d+8) = 1/4
4n = d+8
4n-8 = d _______(ii)
from (i) and (ii)
3n-3 = 4n-8
3n-4n = -8+3
-n = -5
n = 5
putting value of n in equation (i)
3×5-3 = d
12 = d
Required fraction = n/d = 5/12