Question
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 ?
Answer: Option B
Let the man's age be 7x years , Then son's age = 3x years
$$\eqalign{
& \therefore {\text{7}}x \times 3x = 756 \cr
& \Rightarrow 21{x^2} = 756 \cr
& \Rightarrow {x^2} = 756 \cr
& \Rightarrow {x^2} = 36 \cr
& \Rightarrow x = 6 \cr} $$
The ratio of their ages after 6 years
$$\eqalign{
& {\text{ = }}\left( {7x + 6} \right):\left( {3x + 6} \right) \cr
& = \left( {7 \times 6 + 6} \right):\left( {3 \times 6 + 6} \right) \cr
& = 48:24 \cr
& = 2:1 \cr} $$
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Let the man's age be 7x years , Then son's age = 3x years
$$\eqalign{
& \therefore {\text{7}}x \times 3x = 756 \cr
& \Rightarrow 21{x^2} = 756 \cr
& \Rightarrow {x^2} = 756 \cr
& \Rightarrow {x^2} = 36 \cr
& \Rightarrow x = 6 \cr} $$
The ratio of their ages after 6 years
$$\eqalign{
& {\text{ = }}\left( {7x + 6} \right):\left( {3x + 6} \right) \cr
& = \left( {7 \times 6 + 6} \right):\left( {3 \times 6 + 6} \right) \cr
& = 48:24 \cr
& = 2:1 \cr} $$
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