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15 Aug 2016, 03:51
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
35% (03:25) correct
65%
(02:58)
wrong
based on 80
sessions
History
Date
Time
Result
Not Attempted Yet
Ace Transport has acquired two trucks to carry different types of cargo. One costs $70,000; the other costs $52,000. The company expects that the first will last 165,000 miles, after which it can be sold for salvage for about $4,000. The other will fetch the same salvage price, but will last 200,000 miles. The two trucks convoy together, so they always show the same mileage readings. If the value of each truck declines at different constant rates for every mile driven, at what mileage reading will the residual values of the two trucks be equal?
A. 87,500 miles
B. 100,000 miles
C. 107,750 miles
D. 112,500 miles
E. The residual values will never be equal.
A. 87,500 miles
B. 100,000 miles
C. 107,750 miles
D. 112,500 miles
E. The residual values will never be equal.
Senthil1981
Joined: 23 Apr 2015
Last visit: 14 Oct 2021
Posts: 225
Given Kudos: 36
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
15 Aug 2016, 08:37
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Quote:
writing the mileage vs value for both trucks in terms of equation :
Truck 1 : 70,000 = m1 * 165,000 + 4,000 , where m1 is the depreciation $ per mile
Solve for m1 = 0.4
So the depreciation line for Truck 1 is y = 0.4 x + 4,000 , where y is in dollars and x is in mileage.
Similarly for Truck 2 : 52,000 = m2 * 200,000 + 4,000
and this gives m2 = 0.24
and similar line for Truck 2 is y = 0.24 x + 4,000.
The question is where values are same, and in terms of the equation, it's where the two depreciation lines meet.
so solve for x, 0.4 x + 4,000 = 72,000
0.24x + 4,000 = 52,000
gives x = 112,500, which is D.
(this took more than 5 mins to solve
, anyone with faster solution please share.) 
15 Aug 2016, 11:39
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Bunuel
Depreciation is something for which the value of some product goes down year by year..but our question deals with depreciation by miles..
The first truck depreciation = 70000 - 4000 = 66000.
The second truck depreciation = 52000 - 4000 = 48000.
We need to find the depreciation per miles now for each truck..
first truck(FT) = 66000 / 165,000 = 0.4.
Second truck(ST) = 48000 / 200000 = 0.24.
Here we need to check at which option both truck get the same result.
A) The first truck real value is 70000 and it'll depreciate by 87,500 miles * 0.4 ( because per mile we are considering )
70000 - 0.4(87500) = 35000
ST = 52000 - 0.24(87500) = 31000...both are not same...discard
B) FT = 70000 - 0.4(100000) = 30000
ST = 52000 - 0.24(100000) = 28000...both are not same...discard
C) FT = 70000 - 0.4(107,750) = 26900
ST = 52000 - 0.24(107,750) = 26140...both are not same...discard
D) FT = 70000 - 0.4(112,500) = 25000
ST = 52000 - 0.24(112,500) = 25000.. same... now give thanks to the God for getting the correct answer and mark D as the correct option and you'll get more tougher question next..
For typing itself I took 10 mins...
