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Question
The numerator of a fraction is four less than its denominator. If 1 is added to both, is numerator and denominator, the fraction becomes `1/2` Find the fraction.
Solution
Let the numerator of a fraction = x
and the denominator of a fraction = y
According to the condition,
x = y - 4 .....(i)
and `("x + 1")/("y + 1") = 1/2`
⇒ 2(x + 1) = y + 1
⇒ 2x + 2 = y + 1
⇒ 2x - y = -1 ...(ii)
Substitute the eq.(i) in eq.(ii)
2(y - 4) - y = -1
2y - 8 - y = - 1
y = - 1 + 8
y = 7
Now, put the value of y in eq.(i), we get
x = 7 - 4 = 3
∴ The numerator of a fraction is 3
and denominator is 7 and the fraction is `3/7`
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