Question

The numerator of a rational number is less than the denominator by 8. If the denominator is decreased by 1
and numerater is increased by 17, then the number obtained is 3/2 Find the rational number​

Answer 1

Answer:

The rational number = 13/21

Step-by-step explanation:

Given,

• The numerator of a rational number is less than the denominator by 8
• If the denominator is decreased by 1  and numerator is increased by 17, then the number obtained is 3/2

To find,

• the rational number

Solution,

 

Let the denominator be "a"

Then the numerator = (a - 8)

➤ The rational number = numerator/denominator

The rational number = (a - 8)/a

Now,

➟ denominator is decreased by 1,

then new denominator becomes (a - 1)

➟ numerator is increased by 17,

then new numerator becomes (a - 8 + 17) = (a + 9)

➙ The new fraction = (a + 9)/(a - 1)

Given, the number obtained is 3/2

    $\sf \dfrac{a+9}{a-1} =\dfrac{3}{2} \\\\ 2(a+9)=3(a-1) \\\\ 2a+18=3a-3 \\\\ 3a-2a=18+3 \\\\ a=21$

The value of a is 21

⇾ denominator = a = 21

⇾ numerator = a - 8 = 21 - 8 = 13

The rational number = 13/21

Verification :

Condition - If the denominator is decreased by 1  and numerator is increased by 17, then the number obtained is 3/2

     $\sf \dfrac{13+17}{21-1}=\dfrac{3}{2} \\\\ \dfrac{30}{20}=\dfrac{3}{2} \\\\ \dfrac{3}{2}=\dfrac{3}{2} \\\\ LHS=RHS$

Hence verified!