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 $\dfrac{7}{8}$th of what her husband weighed before the course. Form two equations in $x\text{ and }y$, find their weights before taking the dieting course.
(a) Mr. Ahuja = 32 kg and Mrs. Ahuja = 45 kg
(b) Mr. Ahuja = 72 kg and Mrs. Ahuja = 67 kg
(c) Mr. Ahuja = 78 kg and Mrs. Ahuja = 51 kg
(d) Mr. Ahuja = 39 kg and Mrs. Ahuja = 63 kg

Answer 1

Hint: We must first determine the two variables that we need to find. And then, we can form the two equations using the information given in the question. We must then solve these two equations simultaneously to get the values of variables $x\text{ and }y$.

Complete step by step solution:
We are given that the weight of Mr. Ahuja before taking the course is $x$ kg, and the weight of Mrs. Ahuja before taking the course is $y$ kg.
Let us now form the equations, using the information given in the question.
It is given that Mr. Ahuja loses 5 kg after taking the dieting course, and now weighs as much as his wife weighed before the course.
So, the weight of Mr. Ahuja after taking the course = $x-5$ kg.
And, the weight of Mrs. Ahuja before taking the course = $y$ kg.
Thus, we get
$y=x-5...\left( i \right)$
It is also given that Mrs. Ahuja loses 4 kg after taking the dieting course, and now weighs $\dfrac{7}{8}$th of her husband’s weight before the course.
So, the weight of Mrs. Ahuja after taking the course = $y-4$ kg.
And, $\dfrac{7}{8}$th of the weight of Mr. Ahuja before taking the course = $\dfrac{7}{8}x$ kg.
Thus, we get
$y-4=\dfrac{7}{8}x...\left( ii \right)$
So, we have successfully formed 2 equations. Now, let us find the value of $x\text{ and }y$.
Let us now substitute the value of $y$ from equation (i) into equation (ii). Thus, we get
$\left( x-5 \right)-4=\dfrac{7}{8}x$
On simplification, we can get
$x-9=\dfrac{7}{8}x$
$\Rightarrow 8\left( x-9 \right)=7x$
So, we get
$8x-72=7x$
Hence, we can also write
$8x-7x=72$
$\Rightarrow x=72$
Thus, the weight of Mr. Ahuja = 72 kg.
Putting the value of $x$ in equation (i), we get
$y=72-5$
$\Rightarrow y=67$
So, the weight of Mrs. Ahuja is 67 kg.

Hence, option (b) is the correct answer.

Note:
We must clearly understand that with n unique equations, we can find the values of n variables. We must also take care that we need to find the weights of Mr. and Mrs. Ahuja before the dieting course and not after the course.