Question

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added number, its digits are reversed. Find the number.​

Answer 1

Answer:

21

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Answer 2

Given : A two-digit number is 3 more than 4 times the sum of its digits & If 18 is added number, its digits are reversed.

To Find : Find the number ?

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Solution : Let's the original number in the form of 10x + y, where x is the digit in the tenth place and y in its unit place. When the digits are reversed the number will be in the form 10x + y.

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$\pmb{\sf{\underline{According~ to ~the~ ~Given ~Question~:}}}$

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$\qquad{\sf:\implies{10x~+~y~=~3~+~40\bigg(x~+~y\bigg)}}$

$\qquad{\sf:\implies{10x~+~y~=~3~+~4x~+~4y}}$

$\qquad{\sf:\implies{10x~-~4x~=~3~+~4y~-~y}}$

$\qquad{\sf:\implies{6x~=~3~+~3y}}$

$\qquad{\sf:\implies{6x~-~3y~=~3\qquad\qquad\bigg\lgroup{Eqⁿ~1}\bigg\rgroup}}$

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$\qquad{\sf:\implies{\bigg(10x~+~y\bigg)~+~18~=~\bigg(10y~+~x\bigg)}}$

$\qquad{\sf:\implies{\bigg(10x~+~y\bigg)~-~\bigg(10y~+~x\bigg)~=~- 18}}$

$\qquad{\sf:\implies{10x~+~y~-~10y~-~x~=~- 18}}$

$\qquad{\sf:\implies{9x~-~9y~=~- 18}}$

$\qquad{\sf:\implies{9\bigg(x~-~y\bigg)~=~- 18}}$

$\qquad{\sf:\implies{\bigg(x~-~y\bigg)~=~\dfrac{- 18}{9}}}$

$\qquad{\sf:\implies{\bigg(x~-~y\bigg)~=~- 2~~~\qquad\bigg\lgroup{Eqⁿ~2}\bigg\rgroup}}$

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$\qquad{\sf:\implies{x~-~y~=~- 2}}$

$\qquad{\sf:\implies{y~=~x~+~2~~~~~~~~~~~~\qquad\bigg\lgroup{Eqⁿ~3}\bigg\rgroup}}$

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• On putting this values of equation 3 in equation 1 we get,

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$\qquad{\sf:\implies{6x~-~3y~=~3}}$

$\qquad{\sf:\implies{6x~-~3\bigg(x~+~2\bigg)~=~3}}$

$\qquad{\sf:\implies{6x~-~3x~-~6~=~3}}$

$\qquad{\sf:\implies{3x~-~6~=~3}}$

$\qquad{\sf:\implies{3x~=~3~+~6}}$

$\qquad{\sf:\implies{3x~=~9}}$

$\qquad{\sf:\implies{x~=~\dfrac{9}{3}}}$

$\qquad{\sf:\implies{x~=~\cancel\dfrac{9}{3}}}$

$\qquad:\implies{\underline{\boxed{\frak{\purple{x~=~3}}}}}$★

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• Putting the values of x in equation 2

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$\qquad{\sf:\implies{x~-~y~=~- 2}}$

$\qquad{\sf:\implies{3~-~y~=~- 2}}$

$\qquad{\sf:\implies{y~=~3~+~2}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{y~=~5}}}}}$★

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Therefore,

• ${\sf{10~×~3~+~5~=~35}}$

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Hence,

$\therefore\underline{\sf{The ~original ~number ~is~\bf{\underline{35}}}}$