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Question
The sum of the numerator and denominator of a fraction is 8. If 3 is added to both of the numerator and the denominator, the fraction becomes `3/4`. Find the fraction.
Solution
Let the required fraction be `x/y`.
Then, we have:
x + y = 8 ……(i)
And,`( x+3)/(y+3) = 3/4`
⇒4(x + 3) = 3(y + 3)
⇒4x + 12 = 3y + 9
⇒ 4x – 3y = -3 ……(ii)
On multiplying (i) by 3, we get:
3x + 3y = 24
On adding (ii) and (iii), we get:
7x = 21
⇒ x = 3
On substituting x = 3 in (i), we get:
3 + y = 8
⇒ y = (8 – 3) = 5
∴ x = 3 and y = 5
Hence, the required fraction is `3/5` .
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