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The ratio of a man's age and his son's age is 7 : 3 and the product of their ages is 756. The ratio of their ages after 6 years will be ?

15 : 2
22 : 1
311 : 7
413 : 9

Answer:- 1

Explanation:-

Solution:

Let the man's age be 7x years ,
Then son's age = 3x years

\begin{aligned} ∴ 7 x \times 3 x = 756 \\ \Rightarrow 21 x^{2} = 756 \\ \Rightarrow x^{2} = 756 \\ \Rightarrow x^{2} = 36 \\ \Rightarrow x = 6 \end{aligned}

$\eqalign{ & \therefore {\text{7}}x \times 3x = 756 \cr & \Rightarrow 21{x^2} = 756 \cr & \Rightarrow {x^2} = 756 \cr & \Rightarrow {x^2} = 36 \cr & \Rightarrow x = 6 \cr}$
The ratio of their ages after 6 years

\begin{aligned} = (7 x + 6) : (3 x + 6) \\ = (7 \times 6 + 6) : (3 \times 6 + 6) \\ = 48 : 24 \\ = 2 : 1 \end{aligned}

$\eqalign{ & {\text{ = }}\left( {7x + 6} \right):\left( {3x + 6} \right) \cr & = \left( {7 \times 6 + 6} \right):\left( {3 \times 6 + 6} \right) \cr & = 48:24 \cr & = 2:1 \cr}$

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The ratio of their ages after 6 years

\begin{aligned} = (7 x + 6) : (3 x + 6) \\ = (7 \times 6 + 6) : (3 \times 6 + 6) \\ = 48 : 24 \\ = 2 : 1 \end{aligned}

$\eqalign{ & {\text{ = }}\left( {7x + 6} \right):\left( {3x + 6} \right) \cr & = \left( {7 \times 6 + 6} \right):\left( {3 \times 6 + 6} \right) \cr & = 48:24 \cr & = 2:1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

Let the man's age be 7x years ,
Then son's age = 3x years

\begin{aligned} ∴ 7 x \times 3 x = 756 \\ \Rightarrow 21 x^{2} = 756 \\ \Rightarrow x^{2} = 756 \\ \Rightarrow x^{2} = 36 \\ \Rightarrow x = 6 \end{aligned}

$\eqalign{ & \therefore {\text{7}}x \times 3x = 756 \cr & \Rightarrow 21{x^2} = 756 \cr & \Rightarrow {x^2} = 756 \cr & \Rightarrow {x^2} = 36 \cr & \Rightarrow x = 6 \cr}$
The ratio of their ages after 6 years

\begin{aligned} = (7 x + 6) : (3 x + 6) \\ = (7 \times 6 + 6) : (3 \times 6 + 6) \\ = 48 : 24 \\ = 2 : 1 \end{aligned}

$\eqalign{ & {\text{ = }}\left( {7x + 6} \right):\left( {3x + 6} \right) \cr & = \left( {7 \times 6 + 6} \right):\left( {3 \times 6 + 6} \right) \cr & = 48:24 \cr & = 2:1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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