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A certain airline's fleet consisted of 60 type A planes at

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A certain airline's fleet consisted of 60 type A planes at  [#permalink]

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New post 13 Sep 2018, 23:12
Hi,

While the tabular and algebraic approach are discussed, we can look at this question in another way.

So when ever 3 Type A are removed they are replaced with 4 of type B. So every year there will be 1 more aircraft in the fleet than previous year.

And for 60 planes to go to 50 % of its value which is 30 , it would take 10 years. But in 10 years the fleet size would be 60 +1* 10= 70 .
So definitely 30 is way less than 50% of the fleet

In 8 years Type A would be 24 less than today which is = 36 and Total fleet size would be 60+8= 68. But 50% of 68 is 34 but type a is more than 50 %

So in 9 Years it would have reduced by 27 which is 33, and fleet size would be 60+9= 69. 50%* 69= 34.5 So type A less than 50 %

hence D

Or You could set up an equation like this

No of planes in given year n = 60-3n+4n

Essentially We can say no of planes 1 year i.e 1980 = 61 and number of Type A = 60-3n =57 when n =1

So in 6,7,8,9,10 years it will be 66,67,68,69 70 receptively and number of type A aircraft would be 42,39,36,33,30 respectively.

So We see that by year 9 Type A aircraft are less than 50 % of total number of aircraft

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Re: A certain airline's fleet consisted of 60 type A planes at  [#permalink]

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New post 25 Mar 2019, 05:03
From the question, we understand that the increase in the fleet is directly related to the number of years.
For example: End of 1979 Fleet: 60, End of 1980 Fleet : 61 {60 + ( - 3typeA + 4typeB ) } i.e 60 + 1 with 4 type B.
We need to find the year at which the number of Type A planes is lesser than 50 % of the fleet.
To find: No. of Type A planes < .5(60+No of years)

Through the options,
After 8 years : Fleet - 60 + 8 {Type B = (8 * 4) =32 , remaining are the type A planes i.e. 36 planes} 36> .5(68)
After 9 years : Fleet - 60 +9 { Type B = (9*4)= 36 , remaining are the type B planes i.e. 33 planes } Suffiicient, since 33 < .5(69)
Ans : D : 9 Years
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Re: A certain airline's fleet consisted of 60 type A planes at  [#permalink]

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New post 26 Mar 2019, 22:30
x < 50% (x+y) ----> x< y

n = no of years

60 - 3n < 4n
60 < 7n

n >= 9
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Re: A certain airline's fleet consisted of 60 type A planes at   [#permalink] 26 Mar 2019, 22:30

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