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 $\dfrac{7}{8}$ th of what her husband weighed before the course. Form two equations in x and y to find their weights before taking the dieting course.

Let Mr. Ahuja and Mrs. Ahuja weigh x kg and y kg respectively.

After one month,

Mr. Ahuja weighs (x - 5) kg and Mrs. Ahuja weighs (y - 4) kg.

Given,

After one month Mr. Ahuja weighs as much as his wife weighed before the course.

∴ x - 5 = y

⇒ x = y + 5 ………(1)

Given,

Mrs. Ahuja after one month weighs $\dfrac{7}{8}$ th of what her husband weighed before the course.

$\therefore y - 4 = \dfrac{7}{8} \times x \\[1em] \Rightarrow 8(y - 4) = 7x \\[1em] \Rightarrow 8y - 32 = 7x \\[1em] \Rightarrow 8y = 7x + 32 \\[1em] \Rightarrow y = \dfrac{7x + 32}{8} …….(2)$

Substituting value of x from equation (1) in equation (2), we get :

$\Rightarrow y = \dfrac{7(y + 5) + 32}{8} \\[1em] \Rightarrow y = \dfrac{7y + 35 + 32}{8} \\[1em] \Rightarrow 8y = 7y + 67 \\[1em] \Rightarrow 8y - 7y = 67 \\[1em] \Rightarrow y = 67.$

Substituting value of y in equation (1), we get :

⇒ x = 67 + 5 = 72.

Hence, weight of Mr. Ahuja and Mrs. Ahuja are 72 kg and 67 kg respectively.