The output of an enterprise increased by $4$ per cent during a year and by $8$ per cent during the next year. Find the average yearly increase in the output during that period.

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Solution

let the initial output be $x$
Increase in first year $= 4 % o f x$
$= \frac{4}{100} \times x$
$= \frac{x}{25}$
Increase in second year $= 8 % o f x$
$= \frac{8}{100} \times x$
$= \frac{2 x}{25}$
Total Increase
$= \frac{x}{25} + \frac{2 x}{25}$
$= \frac{3 x}{25}$
Now, let the average increase be $M$
$A T P < \frac{x \times 2 \times M}{100} = \frac{3 x}{25}$
$=> M = 6$
$∴ a v e r a g e y e a r l y i n c r e a s e = 6 %$

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The output of an enterprise increased by 4 per cent during a year and by 8 per cent during the next year. Find the average yearly increase in the output during that period.

let the initial output be xIncrease in first year=4% of x=4100×x=x25Increase in second year=8% of x=8100×x=2x25Total Increase =x25+2x25=3x25Now, let the average increase be MATP<x×2×M100=3x25=>M=6∴average yearly increase=6%

The output of an enterprise increased by $4$ per cent during a year and by $8$ per cent during the next year. Find the average yearly increase in the output during that period.