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Find the distribution of numbers if 150 is divided in the ratio of $ 2:3:5 $ .
A. $ 45,55,50 $
B. $ 50,80,20 $
C. $ 30,45,75 $
D. $ 50,40,60 $

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Last updated date: 13th Jul 2024
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Answer
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Hint: We take the ratio of the numbers and use the ratio constant to find the numbers. The addition value of the numbers will give the total value of 150. We simplify the equation to find the value of $ x $ and also the numbers.

Complete step-by-step answer:
The distribution of numbers if 150 is divided in the ratio of $ 2:3:5 $ .
We take $ x $ as the ratio constant and find the numbers.
We get the numbers as $ 2x,3x,5x $ .
The additional value of the numbers will give 150.
Therefore, the addition gives $ 2x+3x+5x=10x $ .
We can now equate $ 10x $ with 150 to get $ 10x=150 $ .
We now divide both sides with 10 to get $ \dfrac{10x}{10}=x=\dfrac{150}{10} $ .
For any fraction $ \dfrac{p}{q} $ , we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $ \dfrac{{}^{p}/{}_{d}}{{}^{q}/{}_{d}} $ .
For our given fraction $ \dfrac{150}{10} $ , the G.C.D of the denominator and the numerator is 10.
 $ \begin{align}
  & 2\left| \!{\underline {\,
  10,150 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5,75 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,15 \,}} \right. \\
\end{align} $
The GCD is $ 2\times 5=10 $ .
Now we divide both the denominator and the numerator with 10 and get $ \dfrac{{}^{150}/{}_{10}}{{}^{10}/{}_{10}}=15 $ .
Therefore, the numbers are 30, 45, 75. The correct option is B.
So, the correct answer is “Option B”.

Note: A ratio is a comparison of two quantities. A proportion is an equality of two ratios. To write a ratio: Determine whether the ratio is part to part or part to whole.