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Roy is 11 years old and his uncle is 59 years old. How many years ago was Roy’s uncle 7 times as old as Roy?

Last updated date: 18th Mar 2023
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Hint: We have to observe the relationship between the ages of Roy and his uncle to solve this problem.

Let the present age of Roy be r = 11 years
And the present age of Roy’s uncle be u = 59 years
From the given information, a few years ago Roy’s uncle was 7 times the age of Roy.
Let those few years = y years.
So ‘y’ years ago Roy age = (11 – y) years and his uncle age = (59 – y) years
$\Rightarrow 59 - y = 7(11 - y)$
\eqalign{ & \Rightarrow 6y = 18 \cr & \Rightarrow y = \dfrac{{18}}{6} \cr}
$\Rightarrow y = 3$
$\therefore$ 3 years ago Roy’s uncle was 7 times as old as Roy.

Note: We have to convert the given information into algebraic equations. We need to observe their present ages and their ages before a few years go accordingly. Then we can easily solve the equation to get the required result.