Question

- The age of a man is three times the sum of
the ages of his two sons, and five years,
hence his age will be double the sum of their
ages. Find his present age.​

Answer 1

Answer:

Step-by-step explanation:

Sum of their ages=x

Father's age=3x

After 5 years,

Sum of their ages=x +10

Father's age=2(x+10)

Equate

3x+5 = 2(x+10)

3x+5=2x+20

3x-2x=20-5

x=15

Father's age=45

Answer 2

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Present age of man is 45 years.

Given :-

The age of a man is three times the sum of the ages of his two sons.

5 years hence, his age will be double the sum of their ages.

To find :-

Present age of man.

Solution :-

Let ,

Man's present age = x years

Present age of 1st son = y years

Present age of 2nd son = z years

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

The age of a man is three times the sum of the ages of his two sons.

➪ x = 3(y+z)

➪ y+z = x/3 ..................(i)

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

5 years hence, his age will be double the sum of their ages

5 years hence,

Man's age = (x+5) years

Age of 1st son = (y+5) years

Age of 2nd son = (z+5) years

➪ x+5 = 2[(y+5)+(z+5)]

➪ x+5 = 2(y+z+10)

[ put y+z = x/3 from eq (i)]

➪ x+5 = 2(x/3 + 10)

➪ x+5 = 2x/3 + 20

➪ x - 2x/3 = 20-5

➪ x/3 = 15

➪ x = 45

† Present age of man is 45 years.

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