Question

my father's age 5 years ago plus twice my age 5 years ago plus three times my father's age now gives 130. what is my father's age?​

Answer 1

Answer:

Let Father's age be x and son's age be y.

Father's age 5 years ago = x - 5

Son's age 5 years ago = y - 5

By first condition,

\begin{gathered}\sf\implies{(x - 5) + 2y = 65} \: \\\sf\implies{x + 2y = 70 \: \: \: ...(1)} \end{gathered}

⟹(x−5)+2y=65

⟹x+2y=70...(1)

By second condition,

\begin{gathered}\sf\implies{(y - 5) + 3x = 130} \: \\ \sf\implies{3x + y = 135 \: \: \: ...(2)}\end{gathered}

⟹(y−5)+3x=130

⟹3x+y=135...(2)

By equation (1)

\begin{gathered}\sf\implies{x + 2y = 70} \\ \sf\implies{x + y = \frac{70}{2} } \: \\ \sf\implies{y = 35 - x} \: \: \end{gathered}

⟹x+2y=70

⟹x+y=

2

70

⟹y=35−x

Putting y = 35 - x in equation (2)

\begin{gathered}\sf\implies{3x + (35 - x) =135 } \\ \sf\implies{3x - x = 135 - 35} \: \: \: \\ \sf\implies{2x = 100} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{x = \frac{100}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{x = 50} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}

⟹3x+(35−x)=135

⟹3x−x=135−35

⟹2x=100

⟹x=

2

100

⟹x=50

{\underline{\boxed{\sf{\red{x = 50 }}}}}

x=50

Putting x = 50 in equation (1)

\begin{gathered}\sf\implies{50+ 2y = 70} \\ \sf\implies{2y = 70 -50 } \\ \sf\implies{2y = 20} \: \: \: \: \: \: \: \: \: \: \\ \sf\implies{y = \frac{20}{2} = 10 }\end{gathered}

⟹50+2y=70

⟹2y=70−50

⟹2y=20

⟹y=

2

20

=10

{\large{\underline{\boxed{\sf{\red{y = 10 }}}}}}

y=10

Hence, Father's age is 50 years.

Step-by-step explanation:

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