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Find a number when multiplied by $5$ exceeds itself by $64$
$A)$$14$
$B)$$16$
$C)$$8$
$D)$$18$

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Last updated date: 23rd May 2024
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Answer
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Hint: First we have to define what the terms we need to solve the problem are.
Since a number is need to be multiplied by X and exceeds itself as $64$ and we need to find that unknown number using some formula; (multiplied term) into X equals to X sum of $64$, and the options are to between the numbers are fourteen, sixteen, eight and eighteen.

Complete step by step answer:
As we see the given question as a number is multiplied by number five and exceeds the number sixty-four; which means five times of unknown X equals the sum of X and sixty-four.
Which is $ \Rightarrow 5X = X + 64$(from the given know things we can able to say this)
Hence further solving the above equation as per the cancelling law or turn the right-hand side X into the left-hand side; as follows $ \Rightarrow 5X = X + 64 \Rightarrow 5X - X = 64$(X will passed into right to left side)
$ \Rightarrow 5X - X = 64 \Rightarrow 4X = 64$(Five subtracts one yield four)
$ \Rightarrow 4X = 64 \Rightarrow X = 16$(Cancelling both sides with respect to four will be left side one will occur and in right side sixteen will occur)
Hence option $B)$$16$is the correct option;
If the other options like X equals the fourteen, eight, eighteen, will be doesn’t have any chances to occur, since by solving in division with repeat to four the term will yield remainder is sixteen
Thus, all other options are eliminated and hence option $B)$$16$ is correct.
So, the correct answer is “Option B”.

Note: Since the unknown term is the multiplied by five times and exceed by sixteen which is sum of sixty-four thus only we make X as the unknown term and formed a formula like $ \Rightarrow 5X = X + 64$
Hence solving this we yield the required resultant.