Question

the denominator of a rational number is greater than its numerator by 8. if the numerator is increased by 17 and the denominator is decreased by 1 ,the number obtained is 3/2.find the rational number with full soluction

Answer 1

Let the Rational be P and Q

Numerator be P
And Denominator be Q

Denominator =Numerator+8
Q= P+8

Q=P+8

By condition.


P+17/Q-1=3/2

2(P+17)=3(Q-1)

4P+34=3Q-1

4P+34=3(P+8)-1

4P+34=3P+24-1

4P-3P=23-34

P= -11

Now Q=P+8

Q= -11+8
Q=-3


Now, Rational No.=P/Q=-11/-3=11/3