Question

if the sum of two numbers is 30 and their ration is 2/3. find the number​

Answer 1

Answer:

The numbers are 18 and 12

Step-by-step explanation:

Let,the numbers be 3x and 2x.

Then, 3x+2x=30. ( given )

5x=30

x = 6

Hence, the numbers are

3x=18

2x=12

Answer 2

Appropriate Question :

• If the sum of two numbers is 30 and their ratio is 2 : 3 . Find the number.

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Given :

• Sum of two numbers is 30

• Ratio of the sum is 2 : 3

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To find :

• The numbers

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Assumption :

Let one of the numbers be x.

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Solution :

From Given -

Sum of two numbers is 30

$\sf\:x~+~Other~number~=~30$

$\sf\color{blue}{\implies~Other~number~=~(30-x)}$

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Now according to the question -

Ratio of the sum of two numbers is 2 : 3

$\sf\therefore\:\frac{One~number}{Other~number}=\frac{2}{3}$

$\sf\implies\:\frac{x}{30-x}=\frac{2}{3}$

Cross multiplying

$\sf\implies\:3x=2(30-x)$

$\sf\implies\:3x=60-2x$

Transposing -2x to LHS it becomes +2x

$\sf\implies\:3x+2x=60$

$\sf\implies\:5x=60$

Transposing 5 to RHS it goes to the denominator

$\sf\implies\:x=\frac{60}{5}$

Reducing the fraction to the lower terms

$\sf\implies\:x=\cancel{\frac{60}{5}}$

$\small{\underline{\boxed{\mathrm{\implies\:x=12}}}}$ ★

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Therefore :

$\tt\:One~number$ = x = $\small\fbox{12}$

$\tt\:Other~number$ = ( 30-x ) = 30 - 12 = $\small\fbox{18}$

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Verification :

Plugging the values in the equation framed earlier -

‎$\sf\therefore\:\frac{One~number}{Other~number}=\frac{2}{3}$

‎$\sf\twoheadrightarrow\:\frac{12}{18}=\frac{2}{3}$

Cross multiplying

$\sf\twoheadrightarrow\: 12 \times 3 = 18 \times 2$

$\sf\twoheadrightarrow\:36=36$

$\bf\twoheadrightarrow\:LHS~=~RHS$

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Henceforth :

⠀‎ ⠀⠀ ⠀⠀ ⠀❒ One number is $\large{\mathfrak\red{12}}$

⠀‎ ⠀⠀ ⠀⠀ ⠀❒‎ Other number is $\large{\mathfrak\red{18}}$

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