# The sum of three times the age of the son and the age of the father is 110. If three times the age of his father is added to the age of son we get 170. Then what is the sum of their age? Find their ages.

**Given :**

The sum of 3 times the age of son and the age of father $= 110$.

Three times the age of his father is added to the age of son we get 170.

**To find :**

We have to find their ages and the sum of their ages.

**Solution :**

Let the age of the son be x and the age of the father be y.

$3x+y=110$...............(i)

If 3 times the age of his father is added to the age of son we get 170.

This implies,

$3y+x=170$..............(ii)

Multiply equation 2 by 3 on both sides,

$3(3y+x)=3(170)$

$9y+3x=510$............(iii)

Subtracting equation 1 from equation 3,

$(9y+3x)-(3x+y)=510-110$

$9y-y+3x-3x=400$

$8y=400$

$y=\frac{400}{8}$

$y=50$

$3x+y=110$

$3x+50=110$

$3x=110-50$

$3x=60$

$x=\frac{60}{3}$

$x=20$

Sum of the ages $= x+y= 20+50=70$

Therefore,

**The age of the son is 20 years and the age of the father is 50 years.**

**The sum of their ages is 70.**

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