Question

Two numbers are in the ratio 2:3 The larger number is 30 more than half of the smaller number . find the number ​

Answer 1

Answer:

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Given ratio, 2:3

Let, x be the constant ratio..

➙ 2x : 3x

And the larger number is 30 more than half of the smaller number.

➡ 3x = 1/2 (2x) + 30

➡ 3x = x + 30

➡ 3x - x = 30

➡ 2x = 30

➡ x = 30/2

➡ x = 15

Now, we got the value of x is 15

Substitute the value of x in the ratios..

⟹ 2x = 2(15) = 30

⟹ 3x = 3(15) = 45

Therefore, the numbers are 30 and 45.

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Step-by-step explanation:

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Answer 2

✯✯ QUESTION ✯✯

Two numbers are in the ratio 2:3 The larger number is 30 more than half of the smaller number . Find the number ..

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✰✰ ANSWER ✰✰

$\implies\tt{Let\:the\:first\:number\:be=2x}$

$\implies\tt{Let\:the\:second\:number\:be=3x}$

➮As Given that the larger number is 30 more than half of the smaller number .So ,

$\implies\tt{3x-\dfrac{2x}{2}=30}$

$\implies\tt{\dfrac{3x}{1}-\dfrac{2x}{2}=30}$

$\implies\tt{\dfrac{6x-2x}{2}=30}$

$\implies\tt{\dfrac{4x}{2}=\dfrac{30}{1}}$

$\implies\tt{x=\dfrac{\cancel{30}\times{\cancel{2}}}{\cancel{4}}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{15}}}$

➥Now ,

$\implies\tt{First\:Number=2(15)}$

$\implies\tt\bold{30}$

$\implies\tt{Second\:Number=3(15)}$

$\implies\tt\bold{45}$

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✔VERIFICATION : -

$\implies\tt{\dfrac{3(15)}{1}-\dfrac{2(15)}{2}=30}$

$\implies\tt{\dfrac{40}{1}-\dfrac{30}{2}=30}$

$\implies\tt{\dfrac{90-30}{2}=30}$

$\implies\tt{\cancel\dfrac{60}{2}=30}$

$\implies\tt{30=30}$

$\green\longmapsto\:\large\underline{\boxed{\bf\red{x}\orange{=}\pink{8}}}$

✺ HENCE VERIFIED ✺