Question

The present age of father is three times the sum of the ages of his two daughters. After 5 years hence, his age will be double the sum of their ages. The present age of the father is:

Answer 1

45 yrs

let father's age be f yrs and age of 2 daughters be x and y respectively

ATQ

f=3(x+y).........1

5 years hence   ; father's age=f+5 and daughter' age be x+5 and y+5 respectively

f+5=2(x+5+y+5)

f=2(x+y+10)-5........2

eq 1=eq 2

2(x+y+10)-5=3(x+y)

on solving we get  x+y = 15

now substitute the value of x+y in eq 1 and

father's age will be 45 yrs

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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