Question

27. Two numbers are in the ratio 3 : 4; if 6 be added to each terms of the ratio, then the new
ratio will be 4:5, then the numbers are
(a) 14, 20
(b) 17, 19
(c)18 and 24 (d) none of these

Answer 1

Given: Two numbers are in the ratio of 3: 4. & If 6 is added to both the numbers the new ratio becomes 4: 5.

Need to find: The numbers?

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❍ Let's Consider that the numbers are 3x and 4x respectively.

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$\underline{\bigstar\:{\pmb{\boldsymbol{By\: the\;Given\; Condition\; :}}}}$⠀⠀

• It is given that, if 6 is added to each term of the ratio then the new numbers ratio will be 4: 5.

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$:\implies\sf \Bigg\{\dfrac{3x + 6}{4x + 6}\Bigg\} = \Bigg\{\dfrac{4}{5}\Bigg\} \\\\\\:\implies\sf 5\Big\{3x + 6\Big\} = 4\Big\{4x + 6\Big\} \\\\\\:\implies\sf 15x + 30 = 16x + 24\\\\\\:\implies\sf 15x - 16x = 24 - 30\\\\\\:\implies\sf \cancel{-}\;x =\cancel{ -}\;6\\\\\\:\implies\underline{\pink{\boxed{\pmb{\frak{x = 6}}}}}\;\bigstar$

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Therefore,

• First number, 3x = 3(6) = 18
• Second one, 4x = 4(6) = 24

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$\therefore{\underline{\textsf{Hence, the numbers are \textbf{Option c) 18, 24} respectively.}}}$

Answer 2

Answer :-

$\:$

• Option (c) 18 and 24 is correct!

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Explanation :-

$\:$

$\underline{\underline{\:\:\:\bigstar{\textsf{\textbf{\:Given\::-\:\:\:}}}}}$

$\:$

• Two numbers are in the ratio 3 : 4

• If 6 be added to each terms of the ratio, then the new ratio will be 4 : 5

$\:$

$\underline{\underline{\:\:\:\bigstar{\textsf{\textbf{\:To\:Find\::-\:\:\:}}}}}$

$\:$

• What are the numbers?

$\:$

$\underline{\underline{\:\:\:\bigstar{\textsf{\textbf{\:Solution\::-\:\:\:}}}}}$

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• Let the first number be 3n and second number be 4n

• Therefore, the ratio is 3n/4n

$\:$

$\underline{\sf{\clubsuit\:According\:to\:the\:Question\::-}}$

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• If 6 be added to each terms of the ratio, then the new ratio will be 4/5

$\:$

Therefore,

$\\ \quad\dashrightarrow\:\sf \dfrac{3n + 6}{4n + 6} = \dfrac{4}{5}$

$\:$

By cross multiplying,

$\\ \dashrightarrow\:\sf 5\big(3n + 6\big) = 4\big(4n + 6\big)$

$\\ \quad\dashrightarrow\:\sf \big(5\big)\big(3n\big) + \big(5\big)\big(6\big) = \big(4\big)\big(4n\big) + \big(4\big)\big(6\big)$

$\\ \dashrightarrow\:\sf 15n + 30 = 16n + 24$

$\\ \quad\dashrightarrow\:\sf 30 - 24 = 16n - 15n$

$\\ \dashrightarrow\:\sf 6 = 1n$

$\\ \quad\dashrightarrow\:\underline{\boxed{\bf{\purple{n = 6}}}}\:\red{\clubsuit}$

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Hence,

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• First number = 3n = 3 × 6 = 18

• Second number = 4n = 4 × 6 = 24

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• Therefore, the numbers are 18 and 24

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