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Suppose that a computer program takes $100$ seconds of execution time on a computer with multiplication operation responsible for $80$ seconds of this time. How much do you have to improve the speed of the multiplication operation if you are asked to execute this program four times faster?

1. $14$ times faster
2. $15$ times faster
3. $16$ times faster
4. $17$ times faster

edited | 238 views

+1 vote
We know, Speed always inversely proportional to time $S\rightarrow \frac{1}{t}$

Here it is given $100sec.$ execution time.

Among which $80 sec$ for Multiplication operation and $20sec.$ for other operation

So, to improve the execution time, we must need to improve Multiplication time.

Other operation time will not change, because these are constant time taken by some hardware operation .

Now , to make it $4$ time faster, time will decrease when speed increase.

So, time will be $\frac{1}{4}$ th of original time, i.e. $25 sec.$

Therefore, time for Multiplication operation $=\left ( 25-20 \right )=5sec$

So, multiplication speed increased $=\frac{80}{5}=16$ times

Hence ans $3)$
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