Question

$\large\underbrace{\textsf{\textbf{Question\;:}}}$

The ratio of two numbers is 3:5. If both the numbers are increased by 5 their ratio becomes 2:3. Find the numbers.​

Answer 1

Gɪᴠᴇɴ:

• Two Number In Ratio → 3 : 5
• When both number increased by 5 so their Ratio → 2 : 3

Fɪɴᴅ:

• Their Numbers.

Sᴏʟᴜᴛɪᴏɴ:

• Let the numbers be 3x and 5x.

➪ 3x + 5x : 5x + 5 = 2 : 3

➪ 3 (3x + 5) = 2 (5x + 5)

➪ 9x + 15 = 10x + 10

➪ x = 5

Then,

• 3x = 3 ༝ 5 = 15
• 5x = 5 ༝ 5 = 25

• Therefore, the numbers are 15 and 25.

Answer 2

☯︎ The numbers are in the ratio of 3:5. So, let the numbers be 3x and 5x.

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

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• If both the numbers are increased by five, their ratio becomes 2:3.

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Therefore,

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$:\implies\sf{\dfrac{3x+5}{5x+5}=\dfrac{2}{3}}\\\\\\\\:\implies\sf{3\{3x+5\}=2\{5x+5\}}\\\\\\\\:\implies\sf{9x+15=10x+10}\\\\\\\\:\implies\sf{9x-10x=10-15}\\\\\\\\:\implies\sf{-1x=-5}\\\\\\\\:\implies\underline{\boxed{\pink{\frak{x=5}}}}{\;\bigstar}$

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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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$\therefore\;{\underline{\sf{Hence,\;the\;two\;numbers\;are\;{\textsf{\textbf{15\;\&\;25}}}}.}}$

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