Question

That two numbers are in ratio 2:3 if 9 is added to each they will be in ratio 3:4 find the numbers ?

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Answer 1

Answer:

Given : Two numbers in the ratio 2 : 3 If 9 is added to each, they will be in the ratio 3:4 .

Need To Find : The numbers .

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❍ Let's consider the two number be 2x and 3x .

Given that,

⠀⠀⠀⠀⠀⠀⠀⠀If 9 is added to each, they will be in the ratio 3:4 .

Then ,

⠀⠀⠀⠀⠀ $\sf{\implies \: Formed\: Equation: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀Now Solving the Formed Equation for the value of x :

⠀⠀⠀⠀⠀ $\sf{\implies \: Formed\: Equation: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

By Cross Multiplication :

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:4(2x + 9 )= 3(3x + 9) }$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:8x + 36 = 9x + 27 }$

⠀⠀⠀⠀⠀ $\sf{\implies \: \: 36-27 = 9x - 8x }$

⠀⠀⠀⠀⠀ $\sf{\implies \: \: 36-27 = x }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 9\: }}}}\:\bf{\bigstar}$

Therefore,

First Number = 2x = 2 × 9 = 18 .

Second Number = 3x = 3 × 9 = 27 .

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Hence,\:The\:two\:numbers\:are\:18\:and\:27\:}}}$

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$\large {\boxed {\sf{\mid{\overline {\underline {\bigstar Verification \:}}}\mid}}}$

As , We have ,

⠀⠀⠀⠀⠀ $\sf{\implies \: Formed\: Equation: \:\dfrac{2x + 9 }{3x + 9} = \dfrac{3}{4}}$

Here :

⠀⠀⠀⠀⠀ $\sf{\implies \: \: x = 9 }$

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: x = 9\: in\:Formed \:Equation \::}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{2\times 9 + 9 }{3\times 9 + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{18 + 9 }{27 + 9} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{27 }{36} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀ $\sf{\implies \: \:\dfrac{3 }{4} = \dfrac{3}{4}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\therefore \bf{\underline { Hence,\:Verified \:}}$

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