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.

Answer 1

Answer: numbers are 4030239

Step-by-step explanation:

Answer 2

ANSWER:

Given:

• Ratio of 2 numbers = 2 : 3
• Ratio after adding 8 to the numbers = 10 : 13

To Find

• The numbers

Solution:

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

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