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Verified answer
Answer:
41.4 %
Step-by-step explanation:
Question: A factory kept increasing its output by the same percentage every year. Find the percentage, if it is known that the output doubles in the last two years.
Solution: Let the initial output be 'x' (before 2 years)
Let the required rate be 'r%'.
At the end of 1st year:
output = x(1 + r/100)
At the end of 2nd year:
output = x(1 + r/100) * (1 + r/100)
= x(1 + r/100)^2
Given: output after 2 year is double of that in the initial year
⇒ x(1 + r/100)^2 = 2x
⇒ (1 + r/100)^2 = 2
⇒ 1 + r/100 = √2 ≈ 1.414
⇒ r/100 = 0.414
⇒ r = 41.4
Hence, required percentage is r% = 41.4 %