Question

Two numbers are in a ratio of 3:5 If 7 is added to each of them then the ratio is 11:16 Find the numbers.


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Answer 1

$\huge\mathbb{ \red {★᭄ꦿ᭄S} \pink{ᴏ}\purple{ʟᴜ} \blue {ᴛ} \orange{ɪ} \green{ᴏɴ★᭄ꦿ᭄}}$

Given that, two numbers are in the Ratio of 3:5.

⠀⠀ ☯ Let's consider that the number be 3x and 5x.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

$\begin{gathered}\sf\underline{\bigstar\; According \ to \ Question \ Now\;:}\\ \\\end{gathered}$

If each number is increased by 7, the ratio becomes 11 : 16.

⠀⠀⠀

Therefore,

⠀⠀

$\begin{gathered}:\implies\sf \dfrac{3x + 7}{5x + 7} = \dfrac{11}{16} \\\\\\:\implies\sf 16(3x + 7) = 11(5x + 7) \\\\\\:\implies\sf 48x + 112 = 55x + 77 \\\\\\:\implies\sf 55x - 48x = 112 - 77 \\\\\\:\implies\sf 7x = 35 \\\\\\:\implies\sf x = \cancel\dfrac{35}{7} \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 5}}}}}\end{gathered}$

Hence,

⠀⠀

First Number, 3(5) = 15

Second Number, 5(5) = 25

⠀⠀⠀⠀

$\therefore\:{\underline{\sf{The \ required \ Numbers \ are \ {\textsf{\textbf{ \red{15 and 25.}}}.}}}}$

$\boxed{\huge \star{{\mathfrak{\red{☠Ñãïtîk \: : hêrë☠}\star}}}}$

⠀⠀⠀

Answer 2

$\huge\mathbb{ \red {★᭄ꦿ᭄S} \pink{ᴏ}\purple{ʟᴜ} \blue {ᴛ} \orange{ɪ} \green{ᴏɴ★᭄ꦿ᭄}}$

Given that, two numbers are in the Ratio of 3:5.

⠀⠀ ☯ Let's consider that the number be 3x and 5x.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀

$\begin{gathered}\begin{gathered}\sf\underline{\bigstar\; According \ to \ Question \ Now\;:}\\ \\\end{gathered}\end{gathered}$

If each number is increased by 7, the ratio becomes 11 : 16.

⠀⠀⠀

Therefore,

⠀⠀

$\begin{gathered}\begin{gathered}:\implies\sf \dfrac{3x + 7}{5x + 7} = \dfrac{11}{16} \\\\\\:\implies\sf 16(3x + 7) = 11(5x + 7) \\\\\\:\implies\sf 48x + 112 = 55x + 77 \\\\\\:\implies\sf 55x - 48x = 112 - 77 \\\\\\:\implies\sf 7x = 35 \\\\\\:\implies\sf x = \cancel\dfrac{35}{7} \\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 5}}}}}\end{gathered} \end{gathered}$

Hence,

⠀⠀

First Number, 3(5) = 15

Second Number, 5(5) = 25

⠀⠀⠀⠀

$\therefore\:{\underline{\sf{The \ required \ Numbers \ are \ {\textsf{\textbf{ \red{15 and 25.}}}.}}}}$

$\boxed{\huge \star{{\mathfrak{\red{☠Hãrshü \: : hêrë☠}\star}}}}$

⠀⠀⠀