Question

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

• A. Mr. Ahuja $=$ 86 kg and Mrs. Ahuja $=$ 67 kg
• B. Mr. Ahuja $=$ 32 kg and Mrs. Ahuja $=$ 67 kg
• C. Mr. Ahuja $=$ 56 kg and Mrs. Ahuja $=$ 67 kg
• D. Mr. Ahuja $=$ 72 kg and Mrs. Ahuja $=$ 67 kg

Answer 1

The correct option is D Mr. Ahuja $=$ 72 kg and Mrs. Ahuja $=$ 67 kg

Given, at the end of which Mr. Ahuja loses $5$ kg and weighs as much as his wife weighed before the course
$=>x-5=y$
$=>x-y=5$ ------ (1)
Also, 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, $8x-8y=40$ ----- equation $\left(3\right)$

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.