Question

The ratio of two numbers is 2:3.If both the numbers are increased by 8 their ratio becomes 10:13.Find the numbers.


pls fast now.​

Answer 1

Given data : The ratio of two numbers is 2:3. If both the numbers are increased by 8 their ratio becomes 10:13.

Solution : Here, according to given, the ratio of two numbers is 2:3

Let, first number be 2x and second number be 3x.

⟹ first number = 2x ----{ 1 }

⟹ second number = 3x ----{ 2 }

Now, after adding 8 to both number becomes,

⟹ first number = 2x + 8

⟹ second number = 3x + 8

Now, according to given {after adding 8 to both numbers, ratio becomes 10:13}

⟹ [2x + 8]/[3x + 8] = 10/13 ----{ 3 }

⟹ 13 * [2x + 8] = 10 * [3x + 8]

⟹ 26x + 104 = 30x + 80

⟹ 26x - 30x = 80 - 104

⟹ - 4x = - 24

⟹ 4x = 24

⟹ x = 24/4

⟹ x = 6

Now put value of x in eq. { 1 } and eq. { 2 }

⟹ first number = 2x

⟹ first number = 2 * 6

⟹ first number = 12

and,

⟹ second number = 3x

⟹ second number = 3 * 6

⟹ second number = 18

Answer : First number is 12 and second number is 18.

Verification : Now put obtained value of first number and second number in equation { 3 }.

⟹ [2x + 8]/[3x + 8] = 10/13

⟹ [ 12 + 8]/[ 18 + 8] = 10/13

⟹ 20/26 = 10/13

⟹ 10/13 = 10/13

Hence, it verified.

Answer 2

ANSWER:

• Given:
• Ratio of 2 numbers = 2 : 3
• Ratio after adding 8 to the numbers = 10 : 13
• To Find
• The numbers

Solution:

$\red{\begin{gathered}\text{We are given that,}\\\\:\longrightarrow\text{Ratio of 2 numbers} =2:3\\\\\text{So, let the numbers be 2x and 3x respectively.}\\\\\text{Now, we are given that,}\\\\:\longrightarrow(2x+8):(3x+8)=10:13\\\\\text{So,}\\\\:\implies(2x+8):(3x+8)=10:13\\\\:\implies\dfrac{2x+8}{3x+8}=\dfrac{10}{13}\\\\\text{On cross-multiplying,}\\\\:\implies13(2x+8)=10(3x+8)\\\\:\implies26x+104=30x+80\end{gathered}}$

$\red{\begin{gathered}\text{On rearranging the terms,}\\\\\implies30x-26x=104-80\\\\:\implies4x=24\\\\:\implies x=\dfrac{24\!\!\!\!\!/^{\:\:6}}{4\!\!\!/}\\\\:\implies x=6\\\\\text{So, the numbers are,}\\\\:\implies1)\:\:2x=2\times6=12\\\\:\implies2)\:\:3x=3\times6=18\\\\\text{\bf{The numbers are 12 and 18 respectively.}}\end{gathered}}</p><p></p><p>$

*Mark As Brainlest*