Mr. and Mrs. Ahuja weigh $x$ kg and $y$ kg respectively. They both take a dieting course, at the end of which Mr. Ahuja loses 5 kg and weighs as much as his wife weighed before the course. Mrs. Ahuja loses 4 kg and weighs $\frac{7}{8}$ th of what her husband weighed before the course. Form two equations in $x$ and $y$, find their weights before taking the dieting course.

The correct option is B Mr. Ahuja= $72$ kg and Mrs. Ahuja= $67$ kg
Given, at the end of dieting course, Mr. Ahuja loses $5$ kg and weighs as much as his wife weighed before the course
$=>x-5=y$
$=>x-y=5$ ...(1)
Mrs. Ahuja loses $4$ kg and weighs $\frac{7}{8}th$ of what her husband weighed before the course.
$y-4=\frac{7}{8}x$
$7x-8y=-32$ ....(2)

Multiplying equation $\left(1\right)$ with $8$ we get,

$8x-8y=40$ ...(3)

Subtracting equation $\left(2\right)$from $\left(3\right)$, we get

$x=72$

Substituting $x=72$ in the equation $\left(1\right)$, we get

$x-y=5=>72-y=5=>y=67$

Hence, Mr Ahuja weighed $72kg$ and Mrs. Ahuja weighed $67$ kg. before the dieting course.