Question

A year hence a father will be 5 times as old as his son. Two years ago the father was 3 times as old his son will be 4 years hence. Find their present ages.​

Answer 1

Answer:

present age of father is 29 and of son is 5.

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Answer 2

Step-by-step explanation:

Let the present ages of the father and the son be x years and y years respectively.

According to the question,

Condition I,

A year hence (after) a father will be 5 times as old as his son.

or,(x+1)=5(y+1)

or,x+1=5y+5

or,x=5y+4

Condition II,

Two years ago, the father was 3 times as old as his son will be 4 years hence.

or,(x−2)=3(y+4)

or,x−2=3y+12

or,x=3y+14

Put value of x from equation (i) in equation (ii), we get,

or,5y+4=3y+14

or,5y−3y=14−4

or,2y=10

or,y=102

∴y=5

Put value of y in equation (i), we get,

or,x=5×5+4

or,x=25+4

∴x=29

So, (x,y) = (29,5)

Therefore, the required age of the father is 29 years and the son is 5 years.