Define ages using ratio

Let the present ages of Amit and Amita be $7x$ and $5x$ respectively.

$\text{Amit} = 7x, \text{Amita} = 5x$

Form the equation

According to the problem, Amit's age 5 years ago is $7x - 5$ and Amita's age 5 years hence is $5x + 5$. Their ratio is $1:1$.

$\frac{7x - 5}{5x + 5} = \frac{1}{1}$

Solve for x

Cross-multiplying, we get $7x - 5 = 5x + 5$. Solving for $x$: $2x = 10$, so $x = 5$.

$x = 5$

Calculate present ages

Amit's present age is $7 \times 5 = 35$ years. Amita's present age is $5 \times 5 = 25$ years.

$\text{Amit} = 35, \text{Amita} = 25$

Find years to reach sum of 72

Let $n$ be the number of years after which the sum of their ages is 72. $(35 + n) + (25 + n) = 72 \Rightarrow 60 + 2n = 72 \Rightarrow 2n = 12 \Rightarrow n = 6$.

$n = 6$