Question

A father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the
daughter, what is the present age of the father?

Answer 1

Answer:

The present age of father is $45$ years.

Step-by-step explanation:

Given the relations between the ages of a father and daughter.

Father is twice as old as his daughter,

$20$ years ago father was ten times the age of daughter.

Since the statements are based on the age of daughter,

let the age of daughter be $x.$

So at present age of father $=2x$ . . . . (1)  (twice the age of daughter).

Twenty years ago age of daughter $=x-20$ .

And it is said that ten times of this is the father's age then.

Therefore age of father twenty years ago $=10(x-20)=10x-200$

Also from (1) we can write the age of father twenty years ago $=2x-20$

That means , twenty years ago

        $10x-200=2x-20\\\\10x-2x=-20+200\\\\8x=180\\\\x=180/8=22.5$

Therefore present age of daughter $=22.5years$

Present age of father $=45\ years$

twenty years ago age of daughter $= 2.5$ years

age of father $=25$ years (which is $10*2.5=25$)

Hence the answer

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