if 1 is subtracted from a numerator of a fraction the result is 3/4 and if 6 is added to the denominator the result is 1/2. Find the fraction.
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if 1 is subtracted from a numerator of a fraction the result is 3/4 and if 6 is added to the denominator the result is 1/2. Find the fraction.
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Let us assume:
• The fraction be x/y.
Where,
x is numerator of the fraction.
y is the denominator of the fraction.
When 1 is subtracted from numerator of a fraction:
(x-1)/y = 3/4
Cross multiplication.
4(x - 1) = 3y
4x 4 = 3y (i)
When 6 is added to the denominator:
x/(y + 6) = 1/2
Cross multiplication.
2x = y + 6
→y=2x-6.
In equation --- (i)
4x - 4 = 3y
Substituting the value of y from eq (ii).
4x - 4 = 3(2x - 6)
4x-4-6x - 18
- 4+18=6x - 4x
14 = 2x
x = 14/2
x=7
Now in equation --- (ii)
y=2x-6
Substituting x
y = (2x 7) - 6
y = 14-6
y = 8
Therefore,
• Fraction = x/y = 7/8.