Question

two numbers are in the ratio 8:13.If 14 is added ti each of the numbers ,the ration becomes 2:3.Find the numbers​

Answer 1

Answer:

• 56,91

Step-by-step explanation:

• 8X, 13X
• (8X+14)/ (13X+14) = 2/3
• 24X+42 = 26X+28
• 2X= 14
• X= 7
• Numbers: 8X= 56, 13X= 91

Answer 2

Solution :-

To Find —

The Orginal number.

Given —

• Ratio of the Numbers = 8 : 13

• Ratio after 14 is added to the numbers = 2 : 3

Concept —

Let the number be 8x and 13x.

So the number in ratio form is $\bf{\dfrac{8x}{13x}}$

According to the question , it said that when 14 is added to the number , the ratio becomes 2 : 3.

Hence, the Equation formed is :-

$\bf{\dfrac{8x + 14}{13x + 14} = \dfrac{2}{3}}$

Now , by solving this Equation we will get the required value.

Calculation :-

Given Equation :-

$\bf{\dfrac{8x + 14}{13x + 14} = \dfrac{2}{3}}$

By solving it , we get :-

$:\implies \bf{\dfrac{8x + 14}{13x + 14} = \dfrac{2}{3}} \\ \\ \\ :\implies \bf{\dfrac{3(8x + 14)}{13x + 14} = 2} \\ \\ \\ :\implies \bf{3(8x + 14) = 2(13x + 14)} \\ \\ \\ :\implies \bf{24x + 42 = 26x + 28} \\ \\ \\ :\implies \bf{24x - 26x = 28 - 42} \\ \\ \\ :\implies \bf{-2x = - 14} \\ \\ \\ :\implies \bf{\not{-}2x = \not{-} 14} \\ \\ \\ :\implies \bf{2x = 14} \\ \\ \\ :\implies \bf{x = \dfrac{14}{2}} \\ \\ \\ :\implies \bf{x = 7} \\ \\ \\ \therefore \purple{\bf{x = 7}}$.

Hence, the value of x is 7.

Now putting the value in the numbers, we get :

First Number :-

$:\implies \bf{8x} \\ :\implies \bf{8 \times 7} \\ :\implies \bf{56} \\ \therefore \purple{\bf{56}}$

First Number = 56

Second Number :-

$:\implies \bf{13x} \\ :\implies \bf{13 \times 7} \\ :\implies \bf{91} \\ \therefore \purple{\bf{91}}$

Second Number = 91

Hence , the original numbers are 49 and 91.