Question

10. Two numbers are in the ratio 5:6. If 6 is subtracted from each, the ratio becomes 2:3. Find the
numbers​

Answer 1

Answer:

1st number = 10 and 2nd number is 12

Step-by-step explanation:

let 1st number is 5x

let 2nd number is 6x

A.T.Q :-

5x-6/6x-6 =2/3

5x-6/2x-2 =2/1

5x-6=4x-4

x-2=0

x=2

1st number is 10

2nd number is 12

Answer 2

Given that, two numbers are in the ratio of 5:6 and if 6 is subtracted from each, the ratio becomes 2:3.

❍ Let the two numbers be 5x and 6x.

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

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• If six is subtracted from both the numbers, the ratio becomes 2:3.

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Therefore,

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$\begin{gathered}:\implies\sf{\dfrac{5x-6}{6x-6}=\dfrac{2}{3}}\\\\\\\\:\implies\sf{15x-18=12x-12}\\\\\\\\:\implies\sf{15x-12x=-12+18}\\\\\\\\:\implies\sf{3x=6}\\\\\\\\:\implies\sf{x=\cancel{\dfrac{6}{3}}}\\\\\\\\:\implies\underline{\boxed{\frak{\pink{x=2}}}}{\;\bigstar}\end{gathered}$

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Hence,

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• First number = 5x, 5(2) = 10
• Second number = 6x, 6(2) = 12

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$\therefore\;{\underline{\sf{Hence,\;the\;numbers\;are\;{\textsf{\textbf{10}}}\;\&\;{\textsf{\textbf{12}}}}.}}$⠀⠀⠀⠀