The ages of two persons are in the ratio of $5 : 7$ . Sixteen years ago, they were in the ratio $3 : 5$ . Find their present ages.

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Solution

Calculation of the present ages:
Let the present age of two persons be $5 x$ and $7 x$ respectively as they are in ratio $5 : 7$ .
16 years back, the ages of the persons were $5 x - 16$ and $7 x - 16$ respectively.
According to the question:
$\begin{array}{rcl} \Rightarrow & \frac{5 x - 16}{7 x - 16} = \frac{3}{5} \end{array} \Rightarrow 5 (5 x - 16) = 3 (7 x - 16) (C r o s s m u l t i p l y i n g b o t h s i d e s) \Rightarrow 25 x - 80 = 21 x - 48 \Rightarrow 25 x - 21 x = 80 - 48 (S e p a r a t i n g t h e v a r i a b l e a n d t h e c o n s \tan t t e r m) \Rightarrow 4 x = 32 ∴ x = 8 (D i v i d i n g b o t h s i d e s b y 8)$
Thus the ages of two persons are $5 \times 8 = 40$ and $7 \times 8 = 56$ respectively.
Final Answer: The present age of two persons are 40 years and 56 years.

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