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Question
The denominator of a fraction is greater than its numerator by 11. If 8 is added to both its numerator and denominator, it becomes `3/4`. Find the fraction.
Solution
Let the required fraction be `x/y`.
Then, we have:
y = x + 11
⇒ y – x = 11 ……(i)
Again, `(x+8)/(y+8) = 3/4`
⇒4(x + 8) = 3(y + 8)
⇒4x + 32 = 3y + 24
⇒ 4x – 3y = -8 ……(ii)
On multiplying (i) by 4, we get:
4y – 4x = 44
On adding (ii) and (iii), we get:
y = (-8 + 44) = 36
On substituting y = 36 in (i), we get:
36 – x = 11
⇒ x = (36 – 11) = 25
∴ x = 25 and y = 36
Hence, the required fraction is `25/36` .
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