Question

A mans age is three times his sons age. Ten years ago his age was five times his sons age. Find current age​

Answer 1

Given :

• A man's age is 3 times of his son's age.
• 10 years ago, his age was 5 times of his son's age.

To find :

• Their present ages.

Solution :

Consider,

• Present age of man = m years
• Present age of son = n years

${\underline{\sf{According\: to\:the\:1st\: condition:-}}}$

• A man's age is 3 times of his son's age.

$\mapsto\sf{m=3n.................(i)}$

${\underline{\sf{According\: to\:the\:2nd\: condition:-}}}$

• 10 years ago, his age was 5 times of his son's age.

10 years ago,

• Age of man = (m-10) years
• Age of son = (n-10) years

$\mapsto\sf{m-10=5(n-10)}$

$\mapsto\sf{m-10=5n-50}$

$\mapsto\sf{3n-10=5n-50\:[put\:m=3n\: from\:eq(i)]}$

$\mapsto\sf{3n-5n=-50+10}$

$\mapsto\sf{-2n=-40}$

$\mapsto\sf{n=20}$

• Present age of son = 20 years

Now , put n = 20 in eq(i) for getting the value of m.

$\mapsto\sf{m=3n}$

$\mapsto\sf{m=3\times\:20}$

$\mapsto\sf{m=60}$

• Present age of man = 60 years

Answer 2

$\huge\sf\pink{Answer}$

☞ Age of Father = 60 years

☞ Age of Son = 20 years

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ A father's age is 3 times his son

✭ Ten years ago his age was 5 times his son

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ Their Present Ages?

$\rule{110}1$

$\huge\sf\purple{Steps}$

Let's Assume that,

$\qquad$◕ Age of father as x

$\qquad$◕ Age of son as y

At Present,

≫ x = 3y$\quad$-eq(1)

Before 10 years,

$\qquad$◕ Age of Father = x-10

$\qquad$◕ Age of son = y-10

$\bullet\:\underline{\textsf{ As Per the Question}}$

➢ $\sf x-10 = 5(y-10)$

➢ $\sf x-10 = 5y-50$

➢ $\sf 3y-10 = 5y-50$

$\sf\bigg\lgroup \because Substituting \ value \ of \ x\bigg\rgroup$

➢ $\sf (-10)+50 = 5y-3y$

➢ $\sf 40 = 2y$

➢ $\sf \dfrac{40}{2} = y$

➢ $\sf \red{y = 20}$

Substituting the given values of y in eq(1)

»» $\sf x = 3(20)$

»» $\sf\orange{ x = 60}$

$\rule{170}3$