Question

The ratio of two numbers is 3:4. When 5 is added to both, the new ratio<br />becomes 4:5. What are number?​

Answer 1

❍ The two numbers are in the ratio 3:4, so, let the numbers be 3x and 4x respectively.

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

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• When 5 is added to both the numbers, then the new ratio becomes 4:5.

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Therefore,

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$:\implies\sf{\dfrac{3x+5}{4x+5}=\dfrac{4}{5}}\\\\\\\\:\implies\sf{5(3x+5)=4(4x+5)}\\\\\\\\:\implies\sf{15x+25=16x+20}\\\\\\\\:\implies\sf{25-20=16x-15x}\\\\\\\\:\implies\underline{\boxed{\pink{\frak{x=5}}}}{\;\bigstar}$

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Hence,

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• First number = 3x = 3(5) = 15
• Second number = 4x = 4(5) = 20

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$\therefore\;{\underline{\sf{Hence,\;the\;two\;numbers\;are\;{\textsf{\textbf{15\;\& 20}}}.}}}$

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