Question

the numerator of a rational number is less than its denominator by 2. the new number becomes 2 /3 , when the numerator is doubled. and the denominator is increased by 12 . find the original number .​

Answer 1

Answer:

Let the numerator of the rational number be x.

Then, the denominator of the rational number =x+3

According to the given condition,

New numerator =3x and new denominator =(x+3)+20=x+23

Given,

x+23

3x

=

8

1

By cross multiplying, we get

8(3x)=x+23

⇒24x=x+23

⇒23x=23 ....[On Transposing]

or x=1

Therefore, numerator of the rational number =1 and denominator =1+3=4.

Hence, the original rational number is

4

1

.

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