If we add 1 to the numerator of a fraction becomes 1/2 and if 5 is subtracted from the denominator, it becomes 1. Find the fraction
Answers
Solution
Given :-
- If we add 1 to the numerator of a fraction becomes 1/2
- if 5 is subtracted from the denominator, it becomes 1.
Find :-
- These fraction
Explanation
Let,
- Numerator be = x
- Denominator be = y
A/C to question,
(If we add 1 to the numerator of a fraction becomes 1/2)
==> (x+1)/y = 1/2
==> 2x - y = -2 --------(1)
Again,
(if 5 is subtracted from the denominator, it becomes 1.)
==> x/(y-5) = 1
==> x - y = -5 ----------(2)
Subtract equ(1) & equ(2)
==> 2x - x = -2 + 5
==> x = 3
Keep Value of x in equ(1)
==> 2 × 3 - y = -2
==> y = 6 + 2
==> y = 8
Hence
- Fraction will be (x/y) = 3/8
_________________
Answer Verification
Case(1).
(If we add 1 to the numerator of a fraction becomes 1/2)
==> (3+1)/8 = 1/2
==> 4/8 = 1/2
==> 1/2 = 1/2
L.H.S. = R.H.S.
Case(2).
(if 5 is subtracted from the denominator, it becomes 1.)
==> 3/(8-5) = 1
==> 3/3 = 1
==> 1 = 1
L.H.S. = R.H.S.
That's proved.
_______________
Given :-
If we add 1 to the numerator of a fraction becomes 1/2
if 5 is subtracted from the denominator, it becomes 1.
TO Find :-
These fraction
Explanation
Let,
Numerator be = x
Denominator be = y
A/C to question,
(If we add 1 to the numerator of a fraction becomes 1/2)
==> (x+1)/y = 1/2
==> 2x - y = -2 --------(1)
Again,
(if 5 is subtracted from the denominator, it becomes 1.)
==> x/(y-5) = 1
==> x - y = -5 ----------(2)
Subtract equ(1) & equ(2)
==> 2x - x = -2 + 5
==> x = 3
Keep Value of x in equation (1)
==> 2 × 3 - y = -2
==> y = 6 + 2
==> y = 8
Hence
Fraction will be (x/y) = 3/8
_________________
Answer Verification
Case(1).
(If we add 1 to the numerator of a fraction becomes 1/2)
==> (3+1)/8 = 1/2
==> 4/8 = 1/2
==> 1/2 = 1/2
L.H.S. = R.H.S.
Case(2).
(if 5 is subtracted from the denominator, it becomes 1.)
==> 3/(8-5) = 1
==> 3/3 = 1
==> 1 = 1
L.H.S. = R.H.S.
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