Q. 44.4( 17 Votes )
The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and denominator, it becomes . Find the fraction.
Let the denominator of the fraction be x.
The numerator is 4 less than the denominator.
∴ The numerator = x – 4.
According to the given condition,
⇒ (Multiplying by x + 1 on both sides)
⇒ (Multiplying by 2 on both sides)
2x – 6 = x + 1
⇒ 2x – x = 1 + 6 (Transposing x to LHS and 6 to RHS)
x = 7
The numerator of the fraction = x – 4 = 7 – 4 = 3
The denominator of the fraction = x = 7
∴ The fraction is .
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