Question

two numbers are in the ratio of 5:3. if each is increased by 10, the ratio between the new numbers formed becomes 7:5. find the original number.
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Answer 1

❍ Two numbers are in the Ratio of 5:3. So, Let the two numbers be 3x and 5x respectively.

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$\underline{\boldsymbol{According\: to \:the\: Question :}}$

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• If each number is increased by 10, the ratio b/w the new number formed becomes 7:5.

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Therefore,

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$:\implies\sf \dfrac{5x + 10}{3x + 10} = \dfrac{7}{5} \\\\\\:\implies\sf 5(5x + 10) = 7(3x + 10) \\\\\\:\implies\sf 25x + 50 = 21x + 70\\\\\\:\implies\sf 4x = 20\\\\\\:\implies\sf x = \cancel\dfrac{20}{4}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\;\bigstar$

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Hence,

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• First number, 3x = 3(5) = 15

• Second number, 5x = 5(5) = 25

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$\therefore{\underline{\sf{Hence, \;the\; numbers\;are\;\bf{15\;and\;25}\; respectively.}}}$

Answer 2

Question :

two numbers are in the ratio of 5:3. if each is increased by 10, the ratio between the new numbers formed becomes 7:5. find the original number.

Answer :

$\sf\pink{given}$

• Ratio of two numbers is 5:3

• When increased each by 10 ratio = 7:5 .

• Original number = ?

• Let the number be 5x and 3x

• When ten added the equation formed =

$\longrightarrow\bf{\dfrac{5x + 10}{3x + 10} =\dfrac{7}{5}}$

$\longrightarrow\bf{5\times ( 5x + 10) =7\times ( 3x + 10)}$

$\longrightarrow\bf{25x + 50 =21x + 70}$

$\longrightarrow\bf{25x - 21x = 70 - 50 }$

$\longrightarrow\bf{4x = 20 }$

$\longrightarrow\bf{x = \dfrac{20}{4} }$

$\longrightarrow\bf\pink{x = 5}$

• Therefore original numbers are :

• 3x =

$\longrightarrow\bf{3\times 5}$

$\longrightarrow\bf\pink{15}$

• 5x =

$\longrightarrow\bf{5\times 5}$

$\longrightarrow\bf\pink{ 25 }$