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 multiplication operation if you are asked to execute this program four times faster?

Total execution time is

$100$ seconds

Time taken by multiplication operation is

$80$ seconds

Time taken by other operations is

$100-80=20$ seconds

Now, the program is required to run $4$ times faster.

So, new execution time should be

$\dfrac{100}{4}=25$ seconds

Other operations still take

$20$ seconds

So, time left for multiplication operation is

$25-20=5$ seconds

Originally multiplication operation takes

$80$ seconds

Now it should take

$5$ seconds

So, required improvement in multiplication speed is

$\dfrac{80}{5}=16$

Hence, multiplication operation must be improved by $16$ times.