Find the value of 32cot² 45-85ec²60 +86t^2 30
Answers
Answer:
option C
Step-by-step explanation:
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.
⠀
\begin{gathered}\underline{\bigstar\:{\pmb{\boldsymbol{By\: the\;Given\; Condition\; :}}}}\\\\\end{gathered}
★
BytheGivenCondition:
BytheGivenCondition:
⠀⠀
It is given that, if 6 is added to each term of the ratio then the new numbers ratio will be 4: 5.
⠀
\begin{gathered}:\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\end{gathered}
:⟹{
4x+6
3x+6
}={
5
4
}
:⟹5{3x+6}=4{4x+6}
:⟹15x+30=16x+24
:⟹15x−16x=24−30
:⟹
−
x=
−
6
:⟹
x=6
x=6
★
⠀
Therefore,
First number, 3x = 3(6) = 18
Second one, 4x = 4(6) = 24
⠀
\therefore{\underline{\textsf{Hence, the numbers are \textbf{Option c) 18, 24} respectively.}}}∴
Hence, the numbers are Option c)