Question

the age of a man is three times the sum of the ages of his two children and five years hence his age will be double the sum of the ages find his present age​

Answer 1

Let the age of man be x,

and sum of ages of his two children be y.

ATQ,

x=3y              (i)

5 years hence,

x+5 = 2(y+10)        (It's y + 10 and not y+5 because it was the sum of ages of children Therefore the 5 years would be different for both, thus there will be 10 years in sum.)

3y+5 = 2y+20     (From (i))

y=15

Therefore, x=3*15

               = 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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