Re: Brand A bike costs twice as much as the Brand B bike
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25 May 2017, 06:37
Suppose the Brand B bike costs x dollars. Then the cost of the Brand A bike must be 2x dollars (as given).
Now, the total expenditure after time t is defined as the (Purchase Cost) + (Maintenance cost till the time t).
From Statement (1) alone, we have that the monthly maintenance cost of the Brand A bike is 5% of its purchase cost. 5% of 2x = (5/100)2x = x/10. Hence, monthly maintenance cost is x/10.
Since we are given that the monthly maintenance cost of Brand B bike equals two times the monthly maintenance cost of the Brand A bike, the former equals 2(x/10) = x/5.
Now, we are required to find the time when the total expenditure (includes purchase cost and maintenance cost) on bike A equals the expenditure on bike B. But, we still do not have the time difference between the two purchases. Hence, we cannot evaluate when the two brands would yield equal costs. Hence, Statement (1) alone is not sufficient.
From Statement (2) alone, we have the required time difference, but we do not have the relation between the maintenance costs of the two bikes. Hence, Statement (2) alone is not sufficient.
With the statements together, we have the required costs in terms of x and, say, the total expenditures equal after n months.
Then the total expenditure on bike A equals
(Purchase cost) + (Maintenance cost) =
2x + (x/10)n
And the total expenditure on the bike B equals
(Purchase cost) + (Maintenance cost) =
x + (x/5)n
The two are equal when 2x + xn/10 = x + xn/5. Dividing both sides by x yields 2 + n/10 = 1 + n/5. Solving the equation for n yields n = 10. Hence, the statements together answer the question. The answer is (C)