Question

The numerator and denominator of a rational number are in the ratio 3:4. If the
denominator is increased by 3, the ratio becomes 3:5. Find the rational number,









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Answer 1

A rational number is in the proportion of two natural numbers.

Let the ratio be $\sf{3:4=3k:4k}$

If the denominator is increased by 3 the ratio becomes $\sf{3k:(4k+3)}$

→ $\sf{3k:(4k+3)=3:5}$

Apply cross multiplication

→ $\sf{15k=3(4k+3)}$

→ $\sf{15k=12k+9}$

→ $\sf{3k=9}$

$\sf{\therefore k=3}$

Therefore, the fraction is $\sf{\dfrac{3k}{4k}}$, which is $\sf{\dfrac{9}{12}}$.

If the denominator of $\sf{\dfrac{9}{12}}$ increases by 3, comes $\sf{\dfrac{9}{15}=\dfrac{3}{5} }$. The solution is true.

Answer 2

Answer:

x=9, y= 12

let let the rational number be x/y

therefore x/y= 3/4 and x/y+3 =3 /5

• x=3y/4---(1)
• solve for 'y'
• 3y/4y+12=3/5
• 15y=12y+36
• 3y=36
• y=12---(2)
• put the value of y in eq (1)
• x=3*12/4
• x=9