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.

5% increase

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5% decrease

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No change

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Data insufficient

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Solution

The correct option is A 5% increase
Let the original production be $x$
Then production in 2003 is $= x - \frac{25}{100} x = \frac{75}{100} x$
And production in 2004 is $= \frac{75}{100} x + \frac{40}{100} \times \frac{75}{100} x$

$= \frac{140}{100} \times \frac{75}{100} x$

$= 1.05 x$
So, overall change in the production $\frac{1.05 x - x}{x} \times 100 = 0.05 \times 100 = 5$ % increase.

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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.

The correct option is A 5% increaseLet the original production be x Then production in 2003 is =x−25100x=75100xAnd production in 2004 is =75100x+40100×75100x =140100×75100x =1.05x So, overall change in the production 1.05x−xx×100=0.05×100=5 % increase.