Question

The product of two numbers is 250 .The numbers are in the ratio 5:10 .Find the numbers.​

Answer 1

Answer:

Let the number be 5x and 10x

A/Q —

5x × 10x = 250

15x = 250

x = 50/3

x = 16 2/3

Step-by-step explanation:

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Answer 2

$✠ \: {\underline{\underline\mathfrak\red{Question:-}}}$

The product of two numbers is 250 .The numbers are in the ratio 5:10 .Find the numbers.

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$✠ \: {\underline{\underline\mathfrak\red{Answer:-}}}$

Let Required numbers are x & y

x × y = 250 ------------------(1)

⠀⠀⠀⠀⠀⠀⠀⠀$:↦ \: \: \bf{ \frac{x}{y} = \frac{5}{10} }$

⠀⠀⠀⠀⠀⠀⠀⠀$:↦ \: \: \bf{ \frac{x}{y} = \frac{1}{2} }$

⠀⠀⠀⠀⠀⠀⠀⠀:↦ 2x = y

⠀⠀⠀⠀⠀⠀⠀⠀⠀y = 2x--------(2)

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Put in Equation (1)

⠀⠀⠀⠀⠀⠀⠀⠀⇒x × y = 250

⠀⠀⠀⠀⠀⠀⠀⠀⇒x × 2x = 250

⠀⠀⠀⠀⠀⠀⠀⠀$⇒\bf{ {2x}^{2} = 250}$

⠀⠀⠀⠀⠀⠀⠀⠀$⇒\bf{ {x}^{2} = \frac{250}{2} }$

⠀⠀⠀⠀⠀⠀⠀⠀$⇒\bf{ {x}^{2} = 125}$

⠀⠀⠀⠀⠀⠀⠀⠀$⇒\bf{ x = \sqrt{125} }$

⠀⠀⠀⠀⠀⠀⠀⠀$⇒\bf{ x = {25 \times 5} }$

⠀⠀⠀⠀⠀⠀⠀⠀$⇒\:{\underline{\boxed{\mathfrak\purple{\bf{ x = + - 5 \times \sqrt{5} }}}}}$

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From equation (2)

⠀⠀⠀⠀⠀⠀⠀⠀⇒ y = 2x

⠀⠀⠀⠀⠀⠀⠀⠀$⇒\bf{ y = \: 2 \times ( + - 5 \times \sqrt{5} )}$

⠀⠀⠀⠀⠀⠀⠀⠀$⇒ \:{\underline{\boxed{\mathfrak\purple{\bf{ y = + - \: 10 \sqrt{5} }}}}}$

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⠀⠀⠀⠀⠀⠀⠀⠀${\boxed{\bf\pink{x = 5 \sqrt{5} \: \: , \: \: y = 10 \sqrt{5} }}}$

${\boxed{\bf\pink{x = - 5 \sqrt{5} \: \: , \: \: y = - 10 \sqrt{5} }}}$

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