SOLUTION: A father is 30 years older than his son however he will be only thrice as old as the son after 5 years what is father's present age ? (a) 40 yrs (b) 30 yrs (c) 50 yrs

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Question 262682: A father is 30 years older than his son however he will be only thrice as old as the son after 5 years what is father's present age ?
(a) 40 yrs (b) 30 yrs (c) 50 yrs (d) none of these
Found 2 solutions by palanisamy, Theo:
Answer by palanisamy(496) About Me  (Show Source):
You can put this solution on YOUR website!
Let the age of the son = x
Then the age of his father = x+30
Given,father will be only thrice as old as the son after 5 years
x+30+5 = 3(x+5)
x+35 = 3x+15
35-15 = 3x-x
20 = 2x
2x = 20
x = 20/2 = 10
Therefore the age of his father = x+30 = 10+30 = 45 years

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f = father's age.
s = son's age.

the father is 30 years older than his son.

f = s + 30

in 5 years, the father will be 3 times as old as his son.

f + 5 = 3 * (s+5)

what is the father's age?

solve these 2 equations simultaneously to get your answer.

solve for f in terms of s in the first equation.

this is already done because the equation states that:

f = s + 30

substitute for f in the second equation.

second equation is:

f + 5 = 3 * (s + 5)

equation becomes:

s + 30 + 5 = 3 * (s + 5)

simplify to get:

s + 35 = 3*s + 15

subtract s from both sides of this equation and subtract 15 from both sides of this equation to get:

20 = 2*s

divide both sides of this equation by 2 to get:

s = 20/2 = 10

from the first equation, we get:

f = s + 30 becomes f = 10 + 30 becomes f = 40

we have:

f = 40
s = 10

substitute f = 40 and s = 10 in both original equations to see if they are true.

f = s + 30 becomes 40 = 10 + 30 becomes 40 = 40 which is true.

f + 5 = 3 * (s + 5) becomes 40 + 5 = 3 * (10 + 5) becomes 45 = 30 + 15 becomes 45 = 45 which is also true.

both equations are true confirming the values for f and s of 40 and 10 are good.