Question

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 to find their weights before taking the dieting course.

Answer 1

Weight of Mr. Ahuja = x kg

and weight of Mrs. Ahuja = y kg.

After the dieting,

x - 5 = y

x - y = 5...(1)

and,

7x - 8y = -32...(2)

Multiplying equation no. (1) by 7, we get

Now subtracting (2) from (3)

From (1)

x - 67 = 5x = 72

Thus, weight of Mr. Ahuja = 72 kg.

and that of Mr. Anuja = 67 kg.