Question

The denominator of a rational number is less than its numerator than 5. If 5 is added to the numerator The new number becomes 11/6. Find the original rational number. ​

Answer 1

Answer:

Let fraction as X

Denominator =X-5

Numerator =X+5

X + 5/X-5 = 11/6

X + 5/X-5 = 11/6

6 (X + 5) = 11(X-5)

6X + 30 = 11X-55

11X-6X = 30+55

5X = 85

X = 85/5 = 17

Therefore,

Numerator = X = 17

And,

Denominator = X - 5 = 17-5 = 12

Fraction = Numerator/Denominator=17/12

Answer 2

Answer:

Let the numerator of the rational number =p

Then, the denominator of the rational number =p+5

When numerator is increased by 6, the new numerator =p+6

When denominator decreased by 3, the new denominator =p+2

According to the question,

p+2

p+6

=

3

5

⟹3p+18=5p+10

⟹2p=8

∴p=4

Numerator =p=4

Denominator=p+5=4+5=9

Original number =

9

4