If I is added to the numerator and to the denominator of a fraction, the value obtained
Is 4/5. If 5 is subtracted from its numerator and from its denominator, the resulting
value is 1/2. Find the fraction.
Answers
Solution
Given :-
- If I is added to the numerator and to the denominator of a fraction,
- If 5 is subtracted from its numerator and from its denominator, the resulting value is 1/2.
Find :-
- These Fraction.
Explanation
Let,
- Numerator be = x
- Denominator be = y.
According to question,
Case 1.
==> (x+1)/(y+1) = 4/5
==> 5×(x+1) = 4×(y+1)
==> 5x - 4y = 4 - 5
==> 5x - 4y = -1_________(1)
Again,
==> (x-5)/(y-5) = 1/2
==> 2×(x-5) = (y-5)
==> 2x - y = -5 + 10
==> 2x - y = 5__________(2)
Multiply by 4 in equ(2)
==> 8x - 4y = 20________(3)
Sub. equ(1) & equ(3)
==> 5x - 8x = -1 - 20
==> -3x = -21
==> x = 21/3
==> x = 7 .
Keep in equ(1)
==> 5×7 - 4×y = -1
==> 4y = 35 + 1
==> 4y = 36
==> y = 36/4
==> y = 9
Hence
- Numerator will be = 7
- Dominator will be = 9
Since
Required Fraction.
- Fraction will be (x/y) = 7/9 .
____________________
Given: If 1 is subtracted from the numerator and from the denominator of a fraction, the value obtained is 1/2. If 1 is added to its numerator and to its denominator, the resulting value is 2/3.
To find: Find the fraction.
Solution:
Let the fraction be x/y, then:
According to the first statement, we get:
x-1/y-1 = 1/2
Solving this, we get:
2(x-1) = y-1
2x - 2 = y - 1
2x - y - 1 = 0 (i)
According to the second statement, we get:
x+1/y+1 = 2/3
Solving this, we get:
3(x+1) = 2(y+1)
3x + 3 = 2y + 2
3x - 2y + 1 = 0 .(ii)
Now solving: 2(i) - (ii), we get:
4x - 2y - 2 = 0
- 3x + 2y - 1 = 0
x - 3 = 0
x = 3
Putting x in (i), we get:
2(3) - y - 1 = 0
6 - y - 1 = 0
y = 5
x/y = 3/5
Answer:
So the fraction is 3/5.