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# The numerator of a fraction is 3 less than its denominator. If the numerator is tripled and the denominator is increased by 2, the value of the fraction obtained is 1/2. What was the original fraction?

Answer :

Let the value denominator be x

Since the numerator is 3 less than its denominator,

⇒ numerator = x-3

When numerator is tripled, new numerator = 3(x-3) = 3x-9

And, when denominator is increased by 2, new denominator = x + 2

Now it is given that,

On cross multiplying, we get,

6x – 18 = x + 2

⇒ 5x = 20

⇒ x = 4

∴Old Denominator = 4

⇒ Old Numerator = x – 3 = 1

Therefore, the original fraction was

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