Question

Aman's age is 3 times his son's age.10 years ago he was five times his son's age.what will be their present age? *​

Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find their present Ages.

$\large\bf\underline{Given:-}$

• Aman's age is 3 times his son's age.10 years ago he was five times his son's age.

$\huge\bf\underline{Solution:-}$

• Let His son's age be x years.

So,

• Aman's age = 3x

༒ According to Question:-

10 years ago Aman was five times his son's age.

⠀⠀⠀⠀⠀10 years ago:-

Age of son = x - 10

Aman age = 3x - 10

➻ 3x - 10 = 5(x - 10)

➻ 3x - 10 = 5x - 50

➻ - 10 + 50 = 5x - 3x

➻ 40 = 2x

➻ x = 40/2

➻ x = 20

Hence,

● His Son's age x = 20 years

● Aman's Age 3x = 3× 20 = 60 years

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Answer 2

$\huge\sf\underline\red{Given\::}$

• Aman's age is 3 times his son's age
• 10 years ago he was five times his son's age.

⠀

$\huge\sf\underline\blue{To\:Find\::}$

• Present ages of Aman and his son

⠀

$\huge\sf\underline\pink{Solution\::}$

Let,

• The present age of son = x years
• Age of Aman = 3x years

⠀

$\large\sf\orange{10\:years\:ago}$

$\large\leadsto\:\:\sf\purple{(3x\:-\:10)\:=\:5(x\:-\:10)}$

$\large\leadsto\:\:\sf\green{3x\:-\:10\:=\:5x\:-\:50}$

$\large\leadsto\:\:\sf\purple{50\:-\:10\:=\:5x\:-\:3x}$

$\large\leadsto\:\:\sf\green{2x\:=\:40}$

$\large\leadsto\:\:\sf\purple{x\:=\:{\Large\frac{\cancel{40}}{\cancel{2}}}}$

$\large\leadsto\:\:\sf\green{x\:=\:20}$

⠀

$\sf\gray{Age\:of\:son}$ = $\sf\underline\red{20\:years}$

⠀

$\sf\gray{Aman's\:age}$ = $\sf\purple{3x}$

⠀⠀⠀⠀⠀⠀⠀= $\sf\green{3\:×\:20}$

⠀⠀⠀⠀⠀⠀⠀= $\sf\underline\red{60\:years}$