The production of cars in a factory decreased by 512% from 2015 to 2016. If the factory produced 1890 cars in 2016, find the number of cars produced by the factory in 2015.
Answers
Answer:
Given:
The production of cars in a factory decreased by 5 1/2% from 2015 to 2016. If the factory produced 1890 cars in 2016.
To find:
The number of cars produced by the factory in 2015.
Solution:
Let's assume "P" represents the no. of cars produced by the factory in 2015.
The no. of cars produced by the factory in 2016 = 1890
The rate of decrease, r = 5\frac{1}{2} \% = \frac{11}{2} \% = 5.5\%521%=211%=5.5%
The no. of years, n = 2016 - 2015 = 1 year
To solve the given problem, we will use the following formula:
\boxed{\bold{A = P [1 + \frac{r}{100} ]^n }}A=P[1+100r]n
where
A = no. of cars produced in 2016
P = no. of cars produced in 2015
r = rate of decrease
n = no. of years
Now, on substituting the given values in the formula above, we get
1890 = P [1 - \frac{5.5}{100} ]^1 }}
\implies 1890 = P [1 - 0.055 ]^1 }}
\implies 1890 = P [0.945 ]^1 }}
\implies P = \frac{1890}{0.945}⟹P=0.9451890
\implies \bold{ P = 2000}⟹P=2000
Thus, the number of cars produced by the factory in 2015 is → 2000.
Step-by-step explanation:
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