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If the product of the two whole number is $336$ and their sum exceeds their difference by $32$ numbers are
$A)42,8$
$B)48,7$
$C)24,14$
$D)21,16$

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Last updated date: 25th Jul 2024
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Answer
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Hint: To solve this question we need to consider two unknown numbers, which are $x$ and $y$. We need to see the conditions given in the problem and as per the condition equation will be formed. Firstly we will multiply the unknown numbers giving the product as $336$, and then will subtract the sum and difference of the number which will result in $32$.

Complete step by step answer:
The question asks us to find the numbers which will give the product as $336$. The condition given The first step is to consider a variable $x$ and another term as $y$. On writing the above explanation mathematically we get:
$\Rightarrow {{1}^{st}}term\times {{2}^{nd}}term=336$
So the first and the second terms are the unknown variable given above which are:
$\Rightarrow x\times y=336$
$\Rightarrow x=\dfrac{336}{y}$
Now the second condition states that the difference between the sum of the unknown number and the difference of the number is $32$. So writing it mathematically we get:
$\Rightarrow \left( x+y \right)-\left( x-y \right)=32$
On calculating the expression in the Left Hand Side, to do this we value after the negative sign change the sign, on doing this we get:
$\Rightarrow x+y-x+y=32$
$\Rightarrow y+y=32$
$\Rightarrow y=\dfrac{32}{2}$
On dividing the number $32$ by $2$ we get:
$\Rightarrow y=16$
So one of the numbers is $16$ . Now to find the second number we will put this above value of $y$ in the expression, $x=\dfrac{336}{y}$. So on calculating the expression we get:
$\Rightarrow x=\dfrac{336}{y}$
Putting the value of $y$ as $16$ , we get:
$\Rightarrow x=\dfrac{336}{16}$
On dividing the numerator with $16$ we get:
$\Rightarrow x=21$
$\therefore $ The two numbers which have product $336$ are $21$ and $16$

So, the correct answer is “Option D”.

Note: We can check whether the answers, which are $21$ and $16$ are correct or not. So for this we will multiply the two numbers and see that the product of the numbers results in the number given in the question which is $336$ in the case given. On writing it mathematically we get:
$\Rightarrow 21\times 16$
$\Rightarrow 336$
Since on multiplying the two numbers we get $336$ as the result, hence the answers we got are correct. Also we can check that the difference of the sum of the numbers and the difference of the numbers are $32$ or not.
$\Rightarrow \left( 21+16 \right)-\left( 21-16 \right)$
$\Rightarrow 37-5$
$\Rightarrow 32$
So the answers we got are correct as all the conditions are getting fulfilled.