Arithmetic

Percentages

Medium

A factory kept increasing its output by the same percentage every year. Find the percentage if it is known that the output has doubled in the last two years. (assume $\sqrt{2} = 1.4142$ )

41.42

100

None of these

✅ Correct Option: 1

Let $r$ = the annual growth rate (as a decimal)

Let initial output = 100 units

After 2 years: Output = $100 \times (1 + r)^2$

Since output doubles in 2 years:

$100 \times (1 + r)^2 = 2 \times 100$

$(1 + r)^2 = 2$

$1 + r = \sqrt{2}$

Using the given value $\sqrt{2} = 1.4142$ :

$1 + r = 1.4142$

$r = 1.4142 - 1$

$r = 0.4142$

$r = 0.4142 = 41.42\%$

The factory increases its output by 41.42% every year.

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A factory kept increasing its output by the same percentage every year. Find the percentage if it is known that the output has doubled in the last two years. (assume 2=1.4142\sqrt{2} = 1.41422​=1.4142)

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A factory kept increasing its output by the same percentage every year. Find the percentage if it is known that the output has doubled in the last two years. (assume $\sqrt{2} = 1.4142$ )