Percent is calculation of quantity per 100 quantity of other thing. The percentage of bikes out of of total surveyed vehicles was 13%
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Assume that total T number of vehicles were surveyed.
Then, as it is given that 70% of the vehicles were cars and 17% were buses.
So, number of cars = [tex]\dfrac{T}{100} \times 70 = \dfrac{7 \times T}{10} = 0.7 \times T[/tex]
Similarly, the number of buses = [tex]\dfrac{T}{100} \times 17 = 0.17 \times T[/tex]
Thus, number of bikes = Total vehicles - number of cars and buses
Number of bikes = T - 0.7T - 0.17T = T(1 - 0.87) = 0.13T
Taking its percentage with total vehicles, let it be x% of total vehicles, then
[tex]0.13T = \dfrac{T}{100} \times x\\\\\text{Multiplying 100/T on both the sides}\\\\13 = x\\x = 13[/tex]
(we could have used short cut that total there is 100%, since number of cars = 70% of total, number of buses = 17% of total, thus
total vehicle's percent being bike = all vehicle (100%) - percent of cars - percent of buses) = (100 - 70 -17)% = 13% )
Thus, the percentage of bikes out of of total surveyed vehicles was 13%
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