During 2003, the production of a factory decreased by 25%. But during 2004, it (production) increased by 40% of what it was at the beginning of 2004. Calculate the resulting change (increase or decrease) in production during these two years.

Let the production of a factory at the beginning of 2003 be 100.

The production of a factory decreased by 25%.

Hence,

Decreased production in 2003 = 100 - 25% of 100

= $100 - \Big(\dfrac{25}{100} \times 100\Big)$

= $100 - \Big(\dfrac{25}{\cancel{100}} \times \cancel{100}\Big)$

= $100 - 25$

= $75$

During 2004, production increased by 40%.

Hence,

Increased production in 2004 = 75 + 40% of 75

= $75 + \Big(\dfrac{40}{100} \times 75\Big)$

= $75 + \Big(\dfrac{2}{5} \times 75\Big)$

= $75 + \dfrac{150}{5}$

= $75 + 30$

= $105$

Resulting change = Final production - Initial production

= 105 - 100

= 05

Resulting change is positive means production is increased.

Percentage change = $\dfrac{\text{Resulting change}}{\text{Initial production}} \times 100$ %

= $\dfrac{5}{100} \times 100$ %

= $\dfrac{5}{\cancel{100}} \times \cancel{100}$%

= $5$ %

Hence, the increase in production is 5%.