Question

my father age 5 years ago plus twice my age now gives 65 . My age 5 years ago plus three times my father age now gives 130 . what is my father age​

Answer 1

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,

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

By second condition,

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

By equation (1)

$\sf\implies{x + 2y = 70} \\ \sf\implies{x + y = \frac{70}{2} } \: \\ \sf\implies{y = 35 - x} \: \:$

Putting y = 35 - x in equation (2)

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

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

Putting x = 50 in equation (1)

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

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

Hence, Father's age is 50 years.

_____________________________________

Answer 2

Answer:

father age is 50 years

so always ask my answer