Question

The age of son 40 years less his father. After 10 years father is age 3 time his son's age. What is his father's present age?​

Answer 1

Solution -

• The age of a son is 40 years less than that of his father .

• After 10 years , the father's age is 3 times his son's age.

We have to find the present age of his father .

Let us start by assigning the present age of his father as x years where x is a variable € N and x ≥ 40

Now , if the age of the father is x, the age of his son is 40 years less or ( x - 40) years.

After 10 years , their ages are -

Age of father = x + 10

Age of son = x - 40 + 10 = x - 30

The age of the father is 3 times his son's age

> x + 10 = 3(x-30)

> x+10=3x-90

>2x=100

>x=50

Answer - The age of his father at present is 50 years .

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Answer 2

Answer:

Given :-

• The age of son is 40 years less than his father.
• After 10 years, father age is 3 times his son's age.

To Find :-

• What is the present age of father.

Solution :-

Let,

$\mapsto \rm{\bold{Present\: age\: of\: father =\: y\: years}}$

$\mapsto \rm{\bold{Present\: age\: of\: son =\: (y - 40)\: years}}$

$\leadsto \sf\bold{\green{After\: 10\: years\: :-}}$

$\mapsto \sf Age\: of\: father =\: (y + 10)\: years$

$\mapsto \sf Age\: of\: son =\: (y - 40 + 10)\: years$

According to the question ,

$\implies \sf (y + 10) =\: 3(y - 40 + 10)$

$\implies \sf y + 10 =\: 3y - 120 + 30$

$\implies \sf y + 10 =\: 3y - 90$

$\implies \sf 10 + 90 =\: 3y - y$

$\implies \sf 100 =\: 2y$

$\implies \sf \dfrac{\cancel{100}}{\cancel{2}} =\: y$

$\implies \sf \dfrac{50}{1} =\: y$

$\implies \sf 50 =\: y$

$\implies \sf\bold{\red{y =\: 50\: years}}$

Hence, the required ages of father and his son are :

$\bigstar\: \: \sf\bold{\purple{Present\: age\: of\: father\: :-}}$

$\longrightarrow \sf y\: years$

$\longrightarrow \sf\bold{\red{50\: years}}$

$\bigstar\: \: \sf\bold{\purple{Present\: age\: of\: son\: :-}}$

$\longrightarrow \sf (y - 40)\: years$

$\longrightarrow \sf (50 - 40)\: years$

$\longrightarrow \sf\bold{\red{10\: years}}$

$\therefore$ The present age of father is 50 years.

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VERIFICATION :-

$\implies \sf y + 10 =\: 3(y - 40 + 10)$

By putting y = 50 we get,

$\implies \sf 50 + 10 =\: 3(50 - 40 + 10)$

$\implies \sf 60 =\: 3(20)$

$\implies \sf \bold{\pink{60 =\: 60}}$

Hence, Verified.