Question

The denominator of a rational number is greater than its numerator by 5. If the numerator is increased by 12and the denominator is decreased by 1, the number obtained is 54 . Find the rational number.

Answer 1

$\sf{Solution :-}$

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 = 4/9

Main Answer :-

=> 4/9